I've installed it on Windows 7 with no problems at all although I'm not sure what the 2008 version of VeSys Classic was that was used (I know I had to patch it with SP0908). Is VeSys Components installed and running? The reason I ask about Components is that its independant from AutoCAD and would demostrate that the installer works (in some way) with Windows 8.
From the description of your problem I doubt that its due to Windows 8 because its unusual to install VeSys with the exception of one exe file. It sounds like the installer simply isn't writing those files to the VeSys directories, I would suggest you contact your distributor or raise a support request to clarify this.
I found this other forum post and suspect that this is related to your problem:
In a response to the above post Nuri stated "VeSys Classic 2008.2 only supports Full AutoCAD (versions 2004-2009)" this would explain why your LTSetup.exe could be missing if you are using that particular installer. To confirm this I would speak to your local support team.
That's interesting Joel, thanks for that link. Support for AutoCAD LT (all versions) was discontinued in 2009, do you know what was the last version of VeSys that supported this?
Its been that long ago I cannot remember what version it was, possibly the one before SP1109?