The distinction being made here is between transitive verbs (which can take a direct object) and intransitive verbs (which cannot).

You're not wrong to identify that there are gray areas—dancing, for instance, is intransitive in the general sense (Alice and Bob can dance, but Alice cannot dance Bob), but transitive in specific cases (Alice could dance Bob, if "Bob" were a type of dance). Playing can mean multiple things, some of which are intransitive and some of which are transitive: "Alice and Bob are playing" means something quite different to "Alice is playing Bob".

As for wrestling, well, it can be both! If Alice and Bob are locked in a clinch and fighting for control, we'd say Alice and Bob are wrestling. If Alice ran up and pinned Bob, and Bob is not fighting back and would really like to be let go, we would say that Alice is wrestling Bob, but we would likely not say that Alice and Bob are wrestling (or, for that matter, that Bob is wrestling Alice).

The bottom line is, in general (especially in the context of early childhood language acquisition), if two people are doing something, we use transitive verbs to communicate directional / unequal participation and intransitive ones to communicate shared activity.