The title made me think you were looking for stuff like QWOP.

Way back I played a bit of A.R.E.S: Extinction Agenda (https://store.steampowered.com/app/92300/ARES_Extinction_Agenda/) - it's a bit of a score attack game, but controls pretty similarly to Abuse.

If purely multiplayer game is your thing, Teeworlds (https://store.steampowered.com/app/380840/Teeworlds/ , https://teeworlds.com/) controls just like Abuse. It's about cure orb-shaped creatures duking it out. It's free, btw.

This is a bit different, but Mari0 has this control scheme. It's Super Mario Bros with a portal gun. There's also a lot of custom levels

Nitro Express

I haven't played it in a while (a decade, even), so I may be mistaken, but I know of Ghost 1.0.

(it's definitely not "modern" though)

Enter the gungeon?

I've recently played Carrion and although you're controlling the monster there it felt very much like Abuse to me. Apart from mouse and keyboard controls, it has very similar art style and art direction with very nice "old school" pixel art. Very mich recommended.

Basically twin stick shooters

I know of some flash/browser games if you're okay with them and know how to safely play them but otherwise, I know I've definitely played a lot of games like this but I'm struggling to remember them.

I haven't played the steam version yet but I know that The Last Stand: Union City is pretty good. It was released on Steam in the Legacy Collection It plays almost like a 2D version of Fallout 3/NV but in a modern setting. I've personally been looking for more games like this but I have yet to find any.

I know it might not be what you are looking for but I know that Terraria plays like this. It starts with melee weapons but you can get ranged weapons and there is a lot of them.

If you are okay with top-down shooters, I'm also aware of a game called Empty Clip.

I'm also aware of some adult games but I don't know if I can post those here.

Shootas Blood and Teef. A 40k themed side scrolling shooter with very heavy stylized graphics. If you like 40k it's a good insight in how orks see themselves. If you don't like 40k it's still a mechanically solid game and it doesn't really have the same grimdarkness that is common in 40k games.

I've been playing DEADBOLT since the demo came out on GameJolt in 2015. Probably my favorite game with a control scheme like that, and it's made by the original devs of Risk of Rain.

Terraria? That could keep you engrossed for a good hundred+ hours 🙂