Text Twist gives you six scrambled letters and about two minutes. Make as many words as you can from them — three letters and up — and find the six-letter word that uses all of them, or the game ends when the timer does. Twist shuffles the letters when you're stuck. It is the word game people who like word games actually play, and it has been on the web since 2001.
This page runs a browser version with the classic timed mode: score for every word, a bonus for the full anagram, and rounds that keep going for as long as you keep solving.
There's no final win — you keep advancing rounds by finding a word that uses all six letters before the timer runs out. The score is cumulative across rounds.
It is one of the few games that genuinely is: it drills anagram recognition and rewards knowing unusual short words. Teachers tend to be fine with it.
Yes. It is a keyboard game that runs in the browser with nothing to install.