Had to think on this for a while.
I think the reason I play games has changed a lot over the years, and it varies depending on what I'm playing. Mostly I play because I enjoy it, and there are very few things in life that I enjoy anymore. Without video games my life would be extremely bleak (well, more bleak than it currently is) and I definitely need that outlet of escapism and stress relief. It's not the same as having fun though, weird as that sounds - I enjoy Monster Hunter, but I wouldn't say that grinding monsters over and over and OVER for crowns is fun. I wouldn't say Rajang was fun either. The experience overall is enjoyable, but there are parts of it that I loathe.
Sometimes I play a game just for the experience. This has become more common as I've gotten older and I'm not as easily impressed as I used to be. It's obvious that very little meets the kind of standard set by Xenoblade Chronicles...and with the possible exception of Tales of Berseria, nothing has even come close to surpassing it. So I've been branching out for the sake of it, and whilst I continue playing if I enjoy myself, I often play because it's something new that I haven't tried yet...this was the case with things like Assassin's Creed, Uncharted, DOOM, etc. I've also played games I know I will hate just so I can criticise them...I've done this with basically every Pokemon game since Platinum. I tried to do it with Persona 4, and I expect at some point I will try again to do it with Persona 4. I'm weird sometimes.
I don't play a game for a challenge as much as I used to because I don't have the time or patience for it. I used to play games for Platinum trophies, but the end result of that was a lot of frustration (Marauder Shields, god why...) and a massive backlog, so I gave up with that a few years back...although sometimes I will still play a game to completion for the sense of satisfaction, as long as that outweighs the overwhelming frustration it generates. But that's a lower priority for me than it used to be, because "challenge" often means bloated HP pools, anti-grind features that just make something longer, or something pathetic like constant instant death spike pits (looking at you, Blasphemous) that just mean it's more time consuming. I've had my "hard mode" phase. Thank god.
So yeah...depends on the game. I have broad reasons, but I tend to approach titles on an individual basis these days. Things I'm unfamiliar with are for the experience, JRPGs are the ones I enjoy, Warriors games are my stress relief, and all of it is to get away from the misery that is often my life. xD