Urgh. That's a shame, then. If these aren't getting to the point where they are actually logging any errors, then we're literally flying blind. There's some problem with the engine, but we didn't code the engine and don't have the source code for it, and it's not reaching our code. It's not a corrupt install (unlike the example at Blendo Games, who also uses Unity and had someone randomly have this problem in 2011 it seems from google).
That pretty well leaves something else on the machine interfering in some fashion, but I have no idea what it could be. The things that come to mind:
1. There's no way it could be a firewall, those just don't mess with programs at the level that could cause this.
2. It is super likely that it's an antivirus or antispyware program, since they actively mess with other processes and can cause all sorts of trouble when they go bad. Do you perhaps have multiple antivirus programs installed without realizing it? Like Windows Defender as well as something else? Maybe a firewall suite came with antivirus as well as the antivirus that you specifically intended to use? Any antispyware programs running constantly in the background?
3. It could be some other program that is trying to interject itself into DirectX/OpenGL programs. Like the Steam overlay does, for instance, although this game of course works fine with that. But there are various other third party things that people use for keeping track of friends while playing games, or for hooking in voice support, or whatever. If one of those is doing something funky with how it is specifically interacts with the Unity engine, then I could see that being a problem.
4. I'm reaching here, but it could be an issue with RAM. Either insufficient RAM at the time of running it (which from the logs it didn't look like that was the case), or a ram chip that is going bad (but that's unlikely because otherwise you'd be seeing generalized freezes and crashes in all sorts of programs).
5. Again reaching, but if you had active spyware or a virus actually running on your machine, then who knows what sort of havoc those could reap. But there again you'd be seeing issues well beyond our game.
6. It could be some sort of graphics driver issue... but honestly I would expect a garbled screen once it gets to having directx and such loaded. This really isn't to that stage yet it doesn't seem -- I don't think it's even loaded directx yet, as mono is just dying well before that.
7. It could be something is wrong with DirectX or OpenGL itself on your machine, but again it seems to be failing too early for that and I would expect larger problems on your system if that were the case.
8. It could be that there is some really funky interaction between this and an installed version of Mono on your machine if you have Mono installed. It would be a first for me to see this, but I guess in theory it's possible that somehow the engine is looking to the global mono dlls in program files rather than looking to its own dlls packaged with the game, and then finding version incompatibilities and dying. But given that mono is compiled right into the engine here, I really don't think that should happen. But very few people have mono installed on their machines, so I guess if there was some sort of interaction that would be fitting that almost nobody ever runs into it with unity games. Still... like 5 people in two years across all of google (and like 1 person per game in question) really seems unlikely low if it were that.
And... that's all I got. I hope one of those triggers some idea for you on what might be the case on your machine...