not quite. you see, it is very simple. a video game can be any or just one of these things, and can be in any state on this chart at any time depending on the context or rearrangement of its elements (mode, ruleset, singleplayer vs multiplayer, etc.). elementary
for science, bc I got into a big argument with my friend group over this, if I were to say something like "video games are intrinsically a form of toy"...how would that make you feel?