Looks like you've got everybody stumped on this one, Mark! Grepping through the old NASM32 include files, I see it referred to as "_TextOutA" and "_TextOutW", apparently. The damn NASMX package is an executable (the Windows version - I've got the Linux version, but it doesn't have "TextOut", of course). Possible it was left out through a "bug"? Can you grep for it?
A very quick test using "-f obj" and "import" (from gdi32.dll) "seems to work" - I don't think it'll actually run. That doesn't help you. If you want to zip up the results of running the NASMX executable and send 'em to me - fbkotler at myfairpoint dot net - I can look. Probably won't see anything... "Should Work", I think...
Best,
Frank