Just look in the animal kingdom to see all sorts of examples, mostly in mammal mating displays.
Some species use loud voices.
Some use ornate dances.
Some decorate homes.
Some smash into each other head first.
There are all sorts of similar displays of skill or strength that are possible without arms. For example imagine some sort of tug of war between two people each holding the rope in their armsteeth. Or a form of wrestling where they try to barge each other out of a ring. The possibilities are endless...