Entertainment/relaxing. They are my main form of both of these.

Rather experience a story than watch/read it.

Good you mentioned fishing first

For me it's a coping mechanism/escape from reality.

I can come home from a gnarly job where I tried to keep a kid alive from a drug overdose or cut someone out of a car... Or scale down a cliff to get someone onto a helicopter and fire up a game and forget it all.

Fishing is the best thing ever.  

For me, it's pure escapism. I want to be immersed in a good story, with good characters, in another world. It's very easy for me to feel as if I'm there, and that's probably why I have always loved gaming.
I've spent so much of my time in these virtual worlds that I've tried to analyze myself to see what it is about.
I think in games you get these idealized versions of concepts like love, friendship, loyalty and such that won't let you down like the real world does, and that appeals to me. Also, you get to mold the world and make it a better place. Especially in RPGs, where you go from town to town and sort out messes and make things right. I'm guessing it gives me a sense of control that I wish I had in the real world, with everything that's going on.

Games do a good job of creating worlds that I dream of. Anime can also do it often and more easily than tv shows/ movies. Books are probably unparalleled but the brain can only think of so much at one time.

I can't physically go back into time to 19th century Japan, but games can help paint a picture.

I can't go to a fantasy world, but games can create nice worlds.

I can't go to space in the years coming, but games can try to imagine a world where you can go to space.

I can't control an entire nation, but games can give you some sort of control.

to have fun

The same, its the stories, and I too view it much like reading a book or watching a movie.
Other than that, I enjoy a good platformer, for the sense of accomplishment of just inputting the right button presses at the right moments to get through a level.... or puzzeling out something slightly tricky (puzzle game, or tower defense), or maybe optimiseing "my own" build path in a rpg. Run off exploreing the world...  So theres differnt elements to differnt genres of games that can appeal to one, each one equally valid.

For people that live less exciting lives than you.... it can be the reverse.
This time your the one on a adventure, scaleing down a cliff ect  (something you wouldn't do in real life).

Because dopamine

To relax.
IRL I'm busy and have a highly stressful job. Gaming gives me a chance to take 1-2 hours and zone out.