Depends on what Operating System the "other computer" is running .
TimeMachine uses ( like everything in OS X ) HFS journaled Filesystem with permission level access for individual files for the user that created it initially.
A modern Linux should mount the disk at least browseable . HFS is supported and well known Filesystem in the Unix world.
Windows does not want to know about HFS . You need a tool like HFSExplorer (free, depends on Java ) or Macdrive ( comercial ) to access Mac volumes in Microsoft environments.