The only thing you need even 1/10th of that power for is going to be 3d rendered emulation, like Naomi games on Demul. For games Mame can actually play, there are a couple that have 3d rendering that will run slow without decent CPU performance, like MK4, but for the most part, anything you will likely play will run just fine. If a game feels slow, hold down the insert key (for mame) to see if you can run faster than the emulation is "supposed" to run.. If you are under 100%, then you need more CPU to run that game at a normal speed. If you are at 400% while holding it down, then you have 4x the power needed to run it. I doubt much of anything in mame will struggle on the machine you are using.
And keep in mind that while you might think a cpu that runs at 1.6ghz is not as fast as one that runs at 4ghz, it is far more dependent on the architecture than the clock speed. The slowest current generation of desktop CPU is still far faster than even the fastest cutting edge stuff made 6-8 years ago.