"game feature" is not a rules-defined term so it's going to be up to your table, your GM, your interpretation of English, and your philosophy on rules-interpretation
Honestly, there is little more to it than that. Lacking any given definition for a "game feature", other than, well, a feature of the game, there is little anybody can hope to go off of. Different tables will have completely different applications of this phrase and there is absolutely nothing wrong with that. Terms simply don't need, and often won't have, any sort of go-to, working, standard, ever-applicable definition.
In fact, the rules themselves are provably inconsistent in the application of this phrase. To quote the Sage Advice Compendium:
Q. Since game features of the same name don’t stack, does that mean a target can’t be affected by a shadow’s Strength Drain more than once between rests?
A. The intended function of Strength Drain is that it stacks with itself, as signaled by the fact that you die if your Strength is reduced to 0 by it.
You'll note that it says the intended function, which means it isn't the written function. It is abundantly clear that Strength Drain is meant to stack but we can see that Strength Drain is a feature of the game and thus actually wouldn't stack under various interpretations of the rules. It is going to be up to the table how they interpret the rules and how they either apply, modify, or ignore that interpretation.
I personally can't tell you what I consider to be a game feature because I don't use a strict definition. All the tables I am in have gone on a case-by-case basis when something in the realm of corner-case-stacking came up. Most of the tables I am at, and have ever been at, have favored case-by-case rulings (with explanation and logic, of course), over hard rules. The reason we've done this is because hard rules often led to even worse complications and corner-cases. Almost all of my tables have determined and accepted that 5e's use of natural language actively lends itself best to a case-by-case, context-dependent analysis of the rules text.