"How would" has no answer
The question "How would wrestling change" is unanswerable. There are many different ways in which a sport could change in a new environment.
As with most sports, "wrestling" is a term used to describe several variants. Most are based around some combination of:
- Forcing an opponent to yield
- Forcing an opponent out of the arena
- Forcing an opponent to make contact with the floor (which part of the body has to touch the floor varies between back, shoulders, hips, or anything but the soles of the feet)
A new environment could also have several variants of wrestling, and although some will quickly be ruled out as impractical or uninteresting, several may persist. Which of the remaining variants last long term will partly be a question of fashion, perhaps in some cases driven more by the popularity of certain contestants than by the popularity of the rule set itself. Of those that happen to remain popular several variants may persist indefinitely.
There is no one predictable answer, just as there is no one best sport.
"How could" has many answers
Having said that, we can still consider the possible directions that adaptation could take in a new environment. For wrestling in free-fall (avoiding the term "microgravity" for its ambiguity), there are many different possibilities, and potentially several of them could be combined in a single sport. Below are listed some variations based on the components of existing wrestling variants.
In general, pinning the opponent to a surface is difficult in free-fall, as explained in Olin Lathrop's answer, but it could be made more feasible:
- Hand and/or foot holds could aid in remaining against the surface
- Making the arena a small room / narrow corridor would allow pushing against the opposite surface
In free-fall it may be easier to have an inverted approach - holding the opponent away from a surface rather than against it. For example, winning by preventing the opponent from making any contact with any surface for 10 seconds.
Pushing the opponent out of a circle (as in Sumo wrestling) or a square (as in Greek wrestling) is less meaningful when moving freely through a 3 dimensional volume. There are analogous methods that could work:
- Force the opponent a given distance from a central location
- Make the opponent touch any wall, even for a moment. The arena could be a hollow sphere with a central hand hold, or a hollow cylinder with a central rail
An alternative location based approach could be to have an arena with 2 ends (such as the inside of a cylinder, or other form of corridor). Then either forcing the opponent to touch either of the end walls gives a win, or each end is assigned to one of the contestants, and the goal is to get the opponent to your end of the arena.
Pinning usually involves not only contact with the floor, but also an element of orientation. For example, one or more of the back, shoulders, or hips may be required to make contact with the floor, depending on the variant of wrestling, usually requiring the opponent to be facing upwards.
Free-fall wrestling could focus on the orientation aspect rather than contact with a surface. This would be less intuitive and more difficult to judge, so it may be combined with some method of measuring whether the achieved orientation is sufficient.
For example, a win may be achieved by preventing an opponent from seeing in a certain direction (contestants could be reading out loud a random single digit number that is displayed on a wall every few seconds, perhaps opposite walls for each contestant). The need for additional methods of measuring orientation may make this kind of variant more likely to quickly pass out of favour.
Making the opponent yield (indicate they accept a loss) is probably the approach that most easily translates from Earth to free-fall. The strategies may be different but the rules would likely be similar to rules on Earth - mainly restricting the ways in which a contestant can attempt to force a yield, to prevent undue risk of injury.
Each of the approaches described above could be used as a single event that defines a win and an end of the match. Alternatively, they could be associated with a number of points being awarded. The match would then continue, with the total number of points being used to determine a winner. The end of the match could then be after a fixed length of time, or when a defined number of points or difference in points has been reached by one player.
Variations near to the question
The methods described above address the question as asked. There are further possibilities if the environment, the equipment, or the number of contestants is varied.
Variations in a rotating habitat.
All of the possibilities listed above assume a non-rotating habitat. In a rotating habitat, occupants can experience something similar to gravity when standing on the curved floor that forms the inside surface. However, the vessel as a whole is still in free-fall, and the contestants will return to experiencing free-fall as soon as they lose contact with the surface. Even a small jump from the surface will give a completely different trajectory than expected based on experience on Earth. For this reason there is some overlap with the kinds of wrestling that are possible in free-fall, with a few extra opportunities for scoring methods. Some of these may in principle also be possible in non-rotating free-fall, but might be more difficult to achieve.
Throwing an opponent on Earth gives an elliptical path (very close to parabolic since the Earth's surface is very close to flat at human scales) that ends quite quickly with collision with the floor. Throwing an opponent when standing on the curved inner surface of a rotating habitat gives a nearly straight line path (since they enter free-fall as soon as you release them) that appears to an observer standing on the curved inner surface to be a conical spiral path in general (with helical paths and near circular paths as special cases). This can lead to arbitrarily long periods before the thrown opponent hits a surface again.
Time of flight
One potential scoring mechanism would be to score points proportional to the time you can leave your thrown opponent stranded waiting to reconnect with the floor.
In addition to the unusual trajectories in a rotating habitat, the apparent weight of the contestants will be decreased if they move along the surface against the direction of rotation, and increased if they move along the surface with the direction of rotation. This allows for throws that appear to require far more than human strength, if the angle and timing are judged carefully.
Disconnection from the floor
Alternatively, simply disconnecting the opponent from the floor (without throwing them) could count for scoring. There could be points proportional to how long they are held away from the floor, or there could be a variant with a single point for holding them away from the floor for a defined length of time.
Variations with magnetic boots and/or gloves
Something nearer to the types of wrestling seen on Earth may be possible if the contestants are equipt with boots and/or gloves that allow them to attach to a suitable surface.
If only certain parts of the surface are magnetic then contestants will need to take this into account in their strategies. For example, if there is only one magnetic area of the surface, then forcing an opponent off the edge of this area will make them easier to move and/or throw.
Variations with more contestants
Instead of trying to pin a single opponent to a floor, the objective could be to separate two opponents from each other. If two teams of two people each start connected (perhaps holding hands, linking arms, or connected to their team-mate by a suitably fragile thread), then the winning team could be the first to force the opposing team to break that connection. In the case of a thread connection, simply breaking the thread is a win. In the case of holding hands or linking arms, a win could result from breaking that hold for a defined number of seconds. Alternatively points could be scored for each second that the opposing team is separated.