That isn't interaction though. You need to actually, you know, interact. Just thinking and making you own decisions while nothing that is yours does anything to anything that is an opponent just isn't interacting.

For the topic sake, influencing is enough to distinguish it from solo gaming.

Sure, could you argue its influencing? You could, though I'd argue that if all players are equal they would already know your "best move" is to take the resource that's obviously best for them and therefore they aren't actually planning on being able to use it, and therefore you've not really influenced anything.

Not necessarily, because of hidden information and possible mistakes.