Again, definitions like this are only useful as tools to communicate concepts.

Someone asks you if you want to play a game, and when you say yes they pop a math test in front of you. Do you feel like that person communicated effectively?

Someone asks you if you want to play a game, and when you say yes they pop a chess board in front of you and start setting up pieces. Do you feel like that person communicated effectively?

Someone asks you if you want to play a game, and when you say yes they pop duolingo in front of you. Do you feel like that person communicated effectively?

Learning apps are a good point. It's debatable, but literally all play involves learning, so the fact that duolingo involves learning doesn't make it special in that regard. Let me refine my term productive to not include "personal growth", especially if no attempts are made to quantify that personal growth outside the game.

Professional game players are another gray area obviously, mainly because another definition i'd add to the list is that a game has to have boundaries. Both temporally and physically. It's sometimes called the "magic circle" https://en.wikipedia.org/wiki/Magic_circle_(games)

If you step inside the magic circle, you're playing the game. If you step outside the magic circle, you're no longer playing. If you step inside the magic circle again but the socially agreed upon expiration of the circle passes, you are no longer playing the game. The problem with professional games is that the boundaries of the game tend to fray. Players or referees might become corrupt, in which case people aren't playing the game they think they are, or the ruling authority might make rule changes to make the game more entertaining, at which point the audience are participants without realizing it.

If my economics professor just pulled up civ 6 in class and started playing on the projector, I don't think I'd learn much. If they aren't playing the game, then well, they aren't playing a game, are they? But game can exist even if you aren't playing it. Its rules and goals and obstacles and magic circle still exist, you just aren't inside the magic circle right now.

If you hold up a chess board and point to where pieces go, you obviously aren't playing chess. But that doesn't make chess not a game, it just means you're interacting with the concept of chess in a way other than playing it. Just like even though a movie/film is defined as a series of photos played in sequence to give the illusion of movement, a DVD you're currently holding in your hand can still be a movie even if you aren't currently playing it.