I looked into the USB-UIRT driver package. Indeed, there appears to be a 64-bit driver (for at least a 64-bit OS)... however, it hasn't been updated since 2009. In fact, the main USB-UIRT driver package itself doesn't look like it's been updated since 2012. More Google searches seem to verify this, no driver updates since 2012 and there's no tech support in general for the USB-UIRT (according to Amazon reviews, for example).
My guess? There could be a bug in the 64-bit driver for a 64-bit Windows OS that prevents it from working (or something else like Windows Updates could have broke it over time). When the driver was created, there were very few 64-bit apps that could use it. Even today, MC23 and MC24 both are just a couple of the handful of Media Center apps that have a 64-bit version available. Also with more Google searching (and searching of the USB-UIRT forums) seems to indicate it doesn't seem to work too well for 64-bit OSes in general, and the ways for getting it working vary like for example
hacking/modifying the drivers and enabling test mode, which in my opinion really isn't a proper solution (not to mention a possible security risk because with test mode unsigned drivers will load).
It working fine with MC24 32-bit is pretty telling, meaning at least for 32-bit the drivers work fine. The downside? Well, since the USB-UIRT hasn't had driver updates in 6 years (and almost 9 years for 64-bit drivers) there's likely nothing JRiver can do about it and is likely incompatible with MC24 64-bit due to lack of proper driver support. For a device to work properly like that, they need to have working drivers. And since the developer isn't releasing driver updates anymore, there's likely nothing JRiver can do about it. My advice? Start looking for alternative IR control that actually receives tech support and driver updates (and has a 64-bit driver available)... or just stick with the 32-bit version of MC. For an older OS like Windows 7, the latter is probably not a bad idea.