I've only seen this icon in Twitch streams, so assume it's something to do with Twitch, but again have only seen this in DOTA2 streams! Any ideas what it is?
This is just the number of charges the streamer's "Pile of Coal" has remaining.
In short, it has nothing to do with Twitch, but it is a consumable item that used to drop from Frostivus Gifts during Greeviling in december 2012. You can use them ingame for a simple animation (coal goes from your hero to the target) with no consequence on gameplay but they have limited use. Most people kept them as a "souvenir" without using charges.