It looks like there is some registry redirection involved here that I'm not aware of.
You can get the installer to work by deleting this key, if it exists:
I think that key would only get written if you installed a 32-bit ooSQLite on a 64-bit system and didn't uninstall it.
That shouldn't apply in my case, so I confess I'm not sure what is going on. In any case, deleting the key will do no harm.