It's purely a relative term, and I like the perspective someone else laid out earlier. Because it can be accurate either way within a narrow spectrum:
"Restored" to operating condition: The machine used to work, but didn't... it's been restored to a functional state that serves its originally intended purpose. For a playable game, this is an acceptable use of the term "restored" as applies to function, even if it has cosmetic blemishes. This is probably all that most players are concerned with.
"Restored" to factory condition: take the above, and fix the cosmetics too. I would agree this is what most collectors are concerned with: a game restored to its original NIB condition.
"Restored = HEP or better": Ha! That's an oxymoron, as no game ever left the factory pimped to that level, therefore none was ever in a HEP-level condition until then, so there was nothing to "REstore". Painted interiors, mirror cabinets, polished mechs, 2PAC vintage pfs? That's not "restored"... that's "modified".
"Restored... but customized..." well now you're into a gray area. A purist won't consider a custom touch as "restored" to factory, even if the condition is "restored" to otherwise like new. So again, see modified.
I like to use the term "refurbished" when describing a whole game when any of its individual sub-components might be "restored". I have "restored" PFs and/or boardsets and put them into unrestored (or partially-restored) cabs. I've restored a bottom cab but not its head or coin door. I've restored a topside pf, but the bottom is merely nice and functional - not shiny new.
I like my games to play like they should and look as nice as I can make them, while retaining some of their historic patina and charm. I wouldn't say any was fully restored, but they're all a hell of a lot better than they were when I got them... so my efforts have to count for something, and it's fair of me to say any of the meriting features are restored. As judged by peers at shows, my games are really nice despite whatever few features aren't perfect, so I leave it up to players / viewers / buyers to compare them against their own priorities.