There are two problems with the question you're asking.
1. The assumption that the purpose of video games is fun.
2. The assumption that everyone has the same universal idea of fun.
Consider an athlete or a performer. Somebody who competes in regional figure skating championships is likely not doing so for fun. Somebody who plays the cello in an orchestra is probably not doing so for fun. Getting good at figure skating or becoming a talented cellist is immensely satisfying and rewarding, but completing these tasks is probably not "fun" for them.
Consider other types of media, as well. Not all music is fun. Not all movies are fun. People's reasons for listening to albums or watching movies are incredibly varied, and the feelings people have when consuming this media are varied equally. The purpose of entertainment and activity is to elicit a desirable response in the participating subject: sadness, fear, pride, accomplishment, tension, relief, excitement, relaxation, etc. Sometimes these sensations overlap with having fun, but often they do not.
Video games are entertainment. They offer a variety of experiences and emotions to the player when consuming them. I would say just as many players enjoy video games as relaxation or to overcome a challenge as they do "fun." Unless I specifically set out to play a game to have fun playing it, whether or not it's fun to play is irrelevant.
I would much rather finish a game and feel like I overcame a challenge ("beat the game") than quit partway through. That isn't satisfying or rewarding to me. That doesn't feel productive or meaningful to me. Satisfied and rewarded or productive and meaningful are all feelings I look for when I choose a video game. It's not always "just for fun."
So, how does this relate to you? Is it possible you're getting something else from your experience other than fun?
Edit: Just corrected a typo over a year later because I'm extremely neurotic.