You need to download and install the build from the Pull Request I linked above. Check the wiki link I posted for instructions where to find the files.
Then open Mixxx, open the library preferences, tick the “Export Serato Metadata” checkbox. Then right click on a track and select “Export Metadata to file tags”. Note that metadata export might be postponed until Mixxx was closed, so better close mixxx before copying the file to a usb stick.
On the other computer, you need a recent build of Mixxx 2.3 beta. You can download Mixxx 2.3 beta from the website (or even install the same build I linked above if you also want to export from the other computer, not only import).
Then load the track into a deck and it should work out of the box in theory (if the track is not yet part of your mixxx library). If the track is already in your library and just just overwrote the file, you need to right-click on the track in Mixxx and reimport metadata from file tags.
If that doesn’t work, let me know here or comment directly on the PR.