Pretty much what the title says. I was going to add some rhythm games I'm playing through, but true completion of the game won't happen for quite a while. Should I log progress for these longer "arcade" styled games?

Don't see why not, generally I'd do it like this

Assuming the game has multiple difficulties it would be:

Core plus a few extras = all songs beat on normal difficulty
Core plus a lot of extras = all songs beat on hard
Completionist = full completion

This is a little harder with something like Osu! which is basically all custom and way more difficulties but you'll have to salt to taste

Since it is pretty much entirely custom, I would consider something like Osu! to fall under "N/A" on the Incomplete - Completion scale, but for games that have a base track list shipped with it, I think @Lahdgren has a good suggestion above. In the end, there's no solid rule and it's up to your personal interpretation. :)

I loge very type of game that i play!

No, because I don't play rhythm games except for Audiosurf.

yup I play but only addicted to geometry dash wave over here https://geometrydashspam.com/

Avid rhythm game player here: I do record rhythm games in my backlog and set a certain goal to consider the game "beaten".

Surprisingly, a lot of rhythm games do have a built-in story that has an end goal, so you can consider those beaten like any other game.

For more open games such as DJ MAX RESPECT V, there's a lot to take in there where there's no story. The base game comes with 200+ songs. Typically playing each song at least once, usually on the same difficulty, is good enough to warrant "playing through the game". I'd say it's also viable for DLCs to have their own entry as well.