Yeah, it's probably because Unity uses the operating system's video API to read the video, so Wine would need mp4/H.264 support. I'll make a Linux build one day if I get the time to allocate to learn installing and building on Linux. I've been unsuccessful the past times I tried some Linux distros (driver compatibility issues every time), but it might work on my new PC?
I've had a great experience with compatible drivers out of the box using Ubuntu (not the coolest distro, but very smooth). Most recently on a Thinkpad. Only thing that didn't work actually was the built-in webcam, but bought a used usb one for very cheap, which works flawlessly.
+ one for a Linux build :)