I am having the same "You can't open the application "TextMate.app" because it is not supported on this architecture."
The installation is under with 10.5.8 on a Dual 2 GHz PowerPC G5.
If it makes any difference, the TextMate update ran while I was logged in as a standard user account. At some point in the process though, I was asked to enter Administrator credentials.
Ever since then, TextMate is dead on this machine.