It depends on whether or not the files are in the format Steam accepts for this purpose: Steam backups.
Here's for example my Team Fortress 2 steam backup:
F:\snip\Steam Backups\Team Fortress 2>tree /F
│ Team Fortress 2_disk1.sim
│ Team Fortress 2_disk1.sis
│ Team Fortress 2_disk1_0.sid
Team Fortress 2_disk2.sim
Team Fortress 2_disk2.sis
Team Fortress 2_disk2_0.sid
(Multiple disks are optional.) If what you have is like that then you can restore the backups merely by using the steambackup.exe file, or alternatively: Steam → Backup and Restore Games → Restore existing backup.
Steam backups are not bound to a specific user, so if you have a friend who has the game installed, he can make a backup for you and that should work.
If that's not what you have, there might still be hope under the form of a Steam Library, but the feature is new (still in the latest Steam Beta at the time of this writing) and thus unlikely to be of much use to you.
This is what a Steam library with Bit Trip Beat in it looks like:
F:\snip\Steam Library>tree /F
│ └───BIT.TRIP BEAT
│ │ (snip)
If this is what you have, you can import it with Steam → Settings → Download and Cloud → Steam Library Folders → Add Library Folder.