Building non-combat stats / doing non-combat things

Yes, it's very open ended. There is a persistent world map gets that filled with randomly generated dungeons. Towns have a job board where you can do a variety of quests for the citizens, like being the entertainment in a party, helping a guy out on his farm, "acquiring" items from others.
As said, all skills affect your character growth. Every skill is assigned an attribute that slowly improves it as you use it more. For example, getting proficient in an instrument increases charisma, which would improve some abilities that use that attribute. Having higher charisma also increases your party size.
It plays like a rogue-like though (numpad, turn-based, identify items) so if that's not up your alley, you won't find it enjoyable. There's a large variety of things to do yet a significant portion of the game consists of rogue-like dungeon crawling, especially if you want to make meaningful progress.

You have unleashed the beast.

Sounds interesting, may check out

I played a bit of the tutorial and it looks interesting, thanks

Make sure you`re playing the latest elona+ version with elona custom installed over it.
bloodyshade.no-ip.org:42333/ElonaCustom/
Just do NOT wear, unappraised gear.
Cursed gear fucks you up in the beginning. They made it cheaper to identify/remove curse of stuff in towns recently, but it`s still fatal to a fresh character.
Also, revive the starter pet if it dies, it`s a bit stronger than you early on and grinding the early levels will be painful whitout their helping hand.
Permadeath mode is a meme, do not play it.

RS has the best memes and reaction images.

Might as well give these too. The game can be rather obtuse for beginners.
elona.wikia.com/wiki/Beginner's_Guide
elona.wikia.com/wiki/Tips

Age of Decadence is designed precisely this way

I made a character with the intention of gathering a harem of loli sex slaves. Anyways, I had my first loli and went to a well. I dunno what happened but my loli got impregnated by an alien. Thinking nothing of it, I just went about my day. Later an alien burst out of my loli's chest then proceeded to kill everyone in the town.

My character died of poison in the side of the road as he was trying to flee to another town during a rainstorm. Lesson of the story is stay away from wells.

Very relevant