The game: TextMate.
The premise: You are given the first few letters of a random word, and your task is to complete the word as fast as possible. Sometimes there could be more than one correct answer, but it doesn't matter. Just finish as quick as possible and get it done before the time runs out.
The other game: Rowowor.
The other premise: This word puzzle game is a little harder to describe. You start out with two letters, and are given 5 more randomly letters one at a time. You must insert the letters to make words. The more words you have made, the more points you score. Gameplay continues until you finish a round with no completed words