Yes "use" is a rather sticky word. Copyright of course covers making copies, but you have to copy software to install it, and as the copy is permanent (unlike say a digital photocopier's buffer) I suspect this is a realistic interpretation. If installing did not count as copying, then I could install one piece of software on an unlimited number of machines.
On the other hand, perhaps the legal mechanism of EULAs is simply that the software won't let you use it until you click "I Agree" - but I would have thought there would be some legal basis where if you don't agree, you have no usage rights, hence it being a "license". It's murky.
I would expect copying to your own computer would fall under fair use, but that copying to a hundred computers would require a hundred purchases. A license mechanism isn't explicitly needed here.
Even installing on 2 computers would be copying 100% of the work, and harm the market for the original work, so I have a hard time seeing this as a fair use.
On the other hand, perhaps the legal mechanism of EULAs is simply that the software won't let you use it until you click "I Agree" - but I would have thought there would be some legal basis where if you don't agree, you have no usage rights, hence it being a "license". It's murky.