I don't have any solid ideas beyond the ones you've already tried, I'm afraid.
I've spent a long time comparing your log to the log from a successful install on Windows 8.1 (64-bit) and, apart from the install path oddity, everything looks about the same up until the point that the uninstaller information is recorded into the registry. (I'm not sure if that is actually important, though. I can't see any errors in your log showing that it tried to write that information but failed, so it seems unlikely it is the cause.)
The log shows the Windows antivirus scanner working through everything the installer is writing just after it writes it, which might be significant. Disabling the scanner may be worth a try. A different installer may also be wroth a try, just in case there's something peculiar going on with a particular file/signature in the one you're using.
(I recommend the 12.2.4 beta installer linked in my signature, if you want to try a different one. It's proven to be a stable release, and the only reason it's still called a beta is there are some English strings that haven't been translated to other languages yet.)
Going back to the install path oddity, was the system migrated from 32-bit to 64-bit at some point int he past, using one of the tools that attempts to do that? That might explain the confusion there.
I also noticed some registry access to do with application compatibility flags, which could be causing both the install path oddity and the overall problem, but may also be perfectly normal. It's hard to tell from what's in the log. Those settings are in the registry but I'm not sure if there is a good way to view them. If you're comfortable using RegEdit, you might want to check under these places:
- Compatibility Assistant
- Compatibility Assistant
and the same HKEY_LOCAL_MACHINE equivalents
for any keys/values with DOpusInstall.exe or ISBEW64.exe in their names.
The ISBEW64.exe one in particular, since it's possible another InstallShield installer triggered compatibility flags to be turned on by the OS automatically for something with the same name.... It's quite a long shot, though.
Peterb's suggestion of trying the install from a different account is a good idea. Sometimes a profile or permissions problem can break things, where a fresh account allows them to succeed. (The program may then work from the main account, or it would at least give us something more to go on.)
The other installer and/or disabling antivirus would be the first things I would try though, since they are the most simple.