In my ~93 days of contributing to the site. I Programming Puzzles & Code Golf has more of a fun / creative aspect but I wouldn't say it ends there. It encourages creative-thinking, and making the most out of what your language can do (which tends to be heavy abuse).
Being able to shrink your code as short as possible may not just help reduce the byte count but provide shorter algorithms. You discover new features, which help you in everyday life when writing code. Sometimes when code golfing you'll code an algorithm that might run in linear time or run just faster.
I'd probably be lying if I said most people didn't come here for fun or green internet points (essentially non practical purposes). It's a creative, and (for me at least) have fun squeezing every byte out of your code.
Since I've joined code-golf, I've been writing more efficient, better code too. While writing with one-letter variable names may just seem obfuscated, you're also creating more short, and concise code.
Then again, they're many other types of challenges, some just requiring out-of the box thinking, and others for real-world practical purposes. So while code-golf may not directly have any practical benefit. It'll help you become a better programmer and really understand your language.