What is the extension on your file? How are you transferring it to the other computer? Any reasonably up-to-date Mac should be able to play exported video from Lightroom out of the box.
I loaded the files onto a usb drive and then transferred the files to the desktop of both of the computers I tried to open the file on. Both computers are using OS 10.11.3
The extensions are the ones established by lightroom and are .m4v