This is a reach, but possible.
Installation is expected to occur under the TrustedInstaller Service context. This is not the same as an elevated admin user. TrustedInstaller can be invoked through a Windows Installer package (MSI) or via legacy installer detection heuristics. This requires that UAC be turned on.
When running this way special 32-bit registry and filesystem redirection takes place to ensure that items are copied and registered in the right places on a 64-bit system.
I'm not an Inno user, but comments I've read suggest that they've tried to get clever and insert an elevation manifest into their setup executable. This blocks the legacy installer detection heuristics in Vista, resulting in the setup running elevated but not under TrustedInstaller.
In addition to having a SysWOW64 there is also a "Program Files (x86)" directory for 32-bit programs. Redirection handles most of the mapping, see
Installation Context.
None of this gets you directly to a solution, but note that turning off UAC and using Inno can interfere with the balance of the ecosystem. Is there a good reason why you aren't using a Windows Installer package?
Otherwise you might consider asking this question in some Inno support forum.
There is really nothing unique about "Ultimate" aside from the extra features you're allowed to install and the ability to join Domains.