Nobody is disagreeing with anyone who says that people play games for different reasons, including agency and a long list of other ones that probably cannot be fully enumerated. Yes, games have different levels of complexity, and clearly more complex games (and there are formal ways to express complexity, though I don't think they're super useful in terms of what we are discussing here) provide the potential for the exercise of agency in more ways or more often, as a general statement. As I said before, we can measure agency and complexity, not perfectly perhaps, but in ways which offer useful comparisons. We can also observe other traits of games and infer things, like the fact that it requires a massive amount of study to reach high competency in Go or Chess indicates high complexity, while our understanding of the game tells us in which places player's express agency (IE what moves to make).
Given a known official dictionary of allowed words, we can also say equally precise things about Scrabble! It also requires a good bit of skill and its highest level players also practice quite a bit from what I understand. However, Scrabble moves don't build on each other in quite the same way that Go or Chess moves do, and there's an obvious element of luck involved as well. Again, there's a very similar sort of agency involved (which of the available legal moves to make).
I don't think it is any great earth-shaking and controversial statement to say that between these three games the agency of the players is fairly similar. They certainly fall within a category or 'zone' of agency in 'strategy board games'. Clearly checkers, backgammon, and lets say Yahtzee, fall into a different zone. There are less possible available board positions and moves which can be made, and they have less overall impact as there are fewer really distinct games of checkers that can exist vs games of chess. This is a lesser zone of agency, and also of complexity. I think in pure 'closed system' board games the two are pretty heavily correlated, though not identical.
RPGs introduce additional considerations, but there's clearly still a sense in which different 'mechanisms of agency' are provided by different games. And so we can certainly again classify them in various ways into groups with different levels of agency. These are going to be arguable, no doubt, but I think it is very likely that some rough consensus exists and that reasons for the choices can be articulated. These are not value judgements about which games are 'good' or 'bad', etc. They aren't even necessarily expressions of preference.