The good news is that WW 2014 from a licensing standpoint is the easiest to work with. They went to Schneider electric in 2017 and Aveva in 2020, both of which use online servers and are a pain.
If your backup is of the entire computer that would be great, as the license files are just text files in the Common Archestra directory and you can copy those over to the new PC. They would have names like WWSUITE.LIC, Archestra.LIC, etc. They will be in the Program Files (x86)\Common Files\Archestra\License folder.
If the backup is just the app, then hopefully you have those license files stored on some media somewhere.
To restore the app is easy. Just copy the application folder to the new computer, launch Intouch Application Manager, click Find Applications and point it to the the folder. Be sure to set your new PC's window resolution to the Intouch application resolution so you don't rescale the application.
Depending on how the application was configured, your backup may or may not have historical files. You can specifiy the application directory or another directory to hold history files. You'll need to open up windowmaker on the restored application, go under configure and then Historical Logging, and see if it using the application directory or a specific folder. If specific, you'll need to create that folder on the new PC.