axiom verge 2, although i'm biased but i think it's pretty underrated
Have you checked out the games in the advertisement thread? Many of them fit your parameters.
One of the things I've posted in that thread is a general call for people to check out pico8 games. All but 3 or 4 of those are doable in under 20 minutes, and they all have free web versions. That'll give you a few dozen to choose from.
If you want fairly quick/easy to complete pico-8 games, I'd suggest Shelled Shinobi, Yarn, willo, Terry the Turtle's Big Adventure, Winterwood, and the any% w/mistakes in Santa Panic.
If you want more of a challenge, check out Ninja Cat & Grippy.
Edit: Note that the pico-8 console allows developers to release their games on Linux by default, so many pico-8 games have Linux versions as well as web versions (often but not always free).
Just do all the web games on MY profile.