I have answered my own question.
I discovered that for some reason the process does not like to be inside too many folders !
My problem was that I had put the extracted folder from the tar.gz inside another on my desktop, instead of extracting the folder itslef to the desktop.

Wrong:
Desktop->WirelessInstalls->RT2870_LinuxSTA_V2.3.0.0

Correct:
Desktop->RT2870_LinuxSTA_V2.3.0.0

The makefile sits inside the RT2870_LinuxSTA_V2.3.0.0 folder.

Whether or not this makes sense, or why it should make any difference at all, I don't know. Nevertheless, I simply extracted the RT2870_LinuxSTA_V2.3.0.0 folder straight to the desktop, opened in terminal, typed checkinstall, and bingo, it all works.

Cheers for anyone who started giving this some thought for me.