I’m wondering if there’s a common name for this word game:
You take a long word and find out how many shorter words you can create using only those letters.
For example, you can take the word “relativity” and find “later,” “ivy,” and “tire.”
I just realized I was calling this an anagram, but an anagram actually scrambles all of the letters from the long word into a different word or sentence.
Am I missing a name, or is this one of those mysterious holes in the English language"
There’s a similar feature in our newspaper by Kathleen Saxe that is, unsatisfyingly, called Word Game. Sorry, I wish I could find a better term too.
Yahoo Games has a version called Text Twist.
There’s no agreed-upon, “technical” term similar to anagram or acrostic. I’d call it a word scramble or something similar.
In a word game book I used to have, they were called “Alphabits”. I love that game and I am wondering where you heard of it and where you can get the game from. Is there a book or a daily newspaper that has it? I remember back in the 70s when I lived in PHilly, the Inquirer had a daily feature just called “Daily Word Game”. Numb.
Astraware distributes a version of Text Twist for PDAs. It’s a fun game – it’s one I always keep on my Palm when I need a little diversion. 
I’ve seen this game called “Word Mine” in several different settings.