Diclaimer: I am not a Lawyer, this is not Legal Advice. Consult a Lawyer if you seek Legal Advice. Additionally, you may want to contact legal@twitch.tv for clarification.
While not directly against the Bits AUP (as far as i can tell), i would argue that this falls under " * Using Bits as a bet or wager or soliciting or accepting Bits for a bet or wager." (at least in those countries where Loot Boxes are considered gambling) since your points are exchangable for these loot boxes.
Regardless of that, I (having made my own Loot Box-based, get-points-for-being-active Chat Bot) highestly recommend you to not intruduce exchanging Bits for your currency in any way shape or form, since this effectively allows people to get your points for something of indirect monetary value, allowing one to associate your points (and thus, your loot boxes and images) with real world monetary value. This means those that obtain and use bits have a clear advantage over those that do not or cannot afford to do this.
You’re introducing Microtransactions to your game. I recommend you not do this.
Having re-read your post more exactly: You say that the viewer choses who the lootbox goes to - so they can’t claim it for themselves. That changes it a bit, but I would still recommend against it, due to the indirect link to real world value.
Also, note that Bits are never used to “buy” or “purchase” something - there is no contract made and nothing is sold. Bits are always “used” or “exchanged”. (Legal kerfuffle, yay)
TL;DR: While not strictly forbidden, I’d recommend against the practice.