After some Googling, I found the solution in this thread on the VirtualBox forums: the sound driver needs to be updated to work in 64-bit Windows. Just download the drivers from the RealTek site, install them in Windows, and reboot. (According to the thread, you may have to then tell Windows to check for updates, install the updates, and reboot again. I don't remember doing this, but I've been so buried in VM apps and Windows that I honestly don't recall.)
After installing the new drivers, sound works as expected.

