Will it be abandoned? Yes. Especially if the game design itself doesn't interesting. Do note, as you said yourself that some people play games to get rid of boredom, but the essential part of gaming itself is whether the game is playful or not, if the game is shitty, people will not play it even if they earn some money. On another hand, people who solely seek profit will come into them. Some popular games like CS GO already have a loyal community, and the game itself is legendary. With that in mind, we know that there is a platform that give the player an earning if they play the game.
I agree, I once be a part of a game that was available in Steam, a gaming website where paid and free games can be downloaded online. It is a game that is kinda boring and not for all and they pushes to make it available in crypto, only few people got interested in the game most of the people just buy the coin because of the people behind it, now the game development is over it is now abandoned.
To put it simply, if the game sucks, people won't play it and there is no money in them since there isn't any gaming/economic activity.
We can argue that if the situation is backward, people could earn a lot in P2E, okay, but will it sustain if the game is uninteresting, very likely no. Some cryptocurrency-centric community seems to forcefully incorporate gaming with cryptocurrencies, while on the other hand, as of now gaming industry does'nt really need cryptocurrency-related technology.
I am eager to see if I'm wrong maybe in the future some gaming companies wether big or indie, are able to make a perfect combination that intersects gaming and cryptocurrency communities, without any hidden motive. Just simply, the game is good.