LemonArcade
No installs and no paywalls: Super Ninja Balloon is a strategy game that starts the second you hit play. It rewards players who plan two moves ahead instead of reacting to the last one. There is a clear Action influence in the design too, giving the game a flavour of its own. And because it is hosted on LemonArcade, it stays unblocked on school networks and Chromebooks.
Build a position patiently, defend the weak points and convert your advantage into victory. A couple of practice runs will teach you more than any instructions.