It allows you to add some pressure to the patty while providing it a restricted space in which it can expand. By doing so the ingredients seem to form a much stronger bond (from my experience). I used to do the same with beef when I ate it.

Also, rolling it into a ball and then wrapping before flattening gives a much better shape to the resulting patty

Pretty common thing to do to help limit cleanup and help shape the patties (regardless of what they're made of).

If you'd rather avoid the single-use-ish plastic, then wax paper usually works as well.