Yes, k is shorthand for a thousand units of something. This is probably based on the numerical prefix "kilo" which means one thousand. It's mostly used informally, I would keep it out of any kind of official or educational paper. Person A: "George, what's your high score on frogger?" George: "Over 860k."

k is short for kilo and yes it means thousand e.g. 1 kilometre is 1000 metres. You can write numbers as 1k, 2k, 10k instead of 1000, 2000, 10000, etc - it is not really correct English but is quite common and most people should understand what you mean.