In a traditional solo video game you're actually interacting with the designer.
In a tabletop or "newer" video game, you're interacting with other people through situations devised by the designer.
Interacting with the designer: (Often called PvE, Player vs. Environment)
Puzzles
Talking with NPCs
Collecting information
Avoiding obstacles and hazards (which may behave sentiently (with intelligence) or not)
Stealth
Con them (bluffing)
Blast/smash them
Clever other methods (drive cattle in front of you)
Dodge/avoid
(Cutscenes–but no interactivity)
Interacting with other people (part of the game, not something the game leads to):
Negotiation (persuade or dissuade)
Direct Conflict (PvP, Player vs. Player)
"Beating them to the punch" (in races, collection of objects, as well as in attacking)
Kill-crush-destroy opposing entities
Physical contests
Cooperation (typical of group RPGs)
Trading
Bidding against/auctioning
Drafting (selecting the best set of useful items, getting something before someone else does)
Anticipation of what someone else will do (could be tied to “beating them to the punch”)
"Bragging rights"
Telling bad jokes, charades, drawing pictures, and many other kinds of party game activities
Acting/pretending (lying) (bluffing)
Being annoying
Indirect interaction (you cause forces other than yours do do something to harm another player's)(e.g. via "Event cards")
Really indirect conflict--you cause forces other than yours to do something to harm other forces that might be helpful to an opponent
In a sense, a great part of interaction with other people could be characterized as “make the right choice before the other person does”.