I had the same problem some time ago.
The answer is that the cheat engine was rewritten recently and now uses individual xml files.
You can grab a new version and have an explanation here.
However, I advise, if you still have, to keep an old MAME version around (with cheat.dat) because sometimes the MAME team seems to like to make changes that break (temporarily) the cheats (see page 4 of the link).
And btw, read the instructions, you don't need to extract the xml files from the cheat.zip archive (happened to a lot of people so I prefer warning you just in case). All you have to do is extract cheat.zip from the archive you download.