The Twitch client updated this add-on along with a bunch of others today, however when I logged into the game (retail) it told me that I had installed the "classic version"... it does appear that 8.6.9 may be classic-specific but Twitch didn't seem to be aware of that. I'm reverting back to 8.6.8 for now but it'd be good if the separation logic either worked or if the classic add-on was separated from the retail one.

Your Twitch App is probably out of date. Try updating it. If that still doesn't help, contact Twitch support. The different versions of TMW properly identify the WoW version they support. If the Twitch app can't handle this properly, Twitch needs to fix it.