it will be valid only for the machine (or more correctly, for the network card in that machine)... this should at least provide a layer of protection against unauthorized use...
Until they upgrade their machine at least, so I hope you have continuing support available for when the app won't work after a motherboard or NIC upgrade...
This can be mitigated a little by checking multiple things about the system, and allowing it to run if 'some' of them match.... That's how XP does it, you can change several hardware components before XP wants re-activation.
MAC address, make/model of the video card, BIOS revision and/or date, CPU ID, amount of memory, harddrive serial number... Plenty of options.