How do I play QuickTime videos stored in iTunes 11?

I have several older videos stored in my iTunes, which is now version 11.1.4. When I try to play them, I get an error message that says QuickTime is no longer supported by this version of iTunes. The only Apple Support article I've found on this issue tells me to download QuickTime, but when I follow the link, Apple tells me that I have the current version of QuickTime in my OS (10.7.5). Seems like a feedback loop, and I'm frustrated. Anyone got a solution?