A couple of comments:

Social interaction is definitely a core activity, but I specifically excluded it from the rules for my current game.  I prefer such things to be done free-form and I've never found a set of rules that provided a better experience than this.

Similarly, problem solving is core, but I consider that a player rather than a character activity.  Anything involving decision-making should not be resolved with a die roll.

Magic is problematic to classify.  On the one hand, it makes sense to call it core.  On the other hand, any time you are using magic, you are trying to do something that can be better described as part of another core activity, like combat, travel, social, etc.  I would tend not to include it in a list of core activities for this reason.

My list would probably be combat, social, stealth, chase, travel, athletics (climb, jump, swim, etc), investigative, exploration (in the strict sense of "go someplace and see what's there"), and environmental survival,  And as I mentioned, not all of those actually need rules.