Take the NES, the Super NES and say, the PlayStation, they all have something in common : games on PAL regions were about 16.7% slower than their NTSC counterpart.
Sure? Any proof for that? They did display maybe 16% less pictures per second, but so does every US TV show aired in Europe. To me no of the actors seam like pumped with tranquillizers.
Now if on you play an arcade game, let's say Pang 3, the ROM for Europe region runs at the exact same speed than the ROM for Japan region.
Well, it isn't a ROM, but a game board that does the display. And most important here, they use the same board in Europe than in the US or Japan. The software (ROM - but more often than not EPROM) differs only for on screen language - if at all, as some games can be switched between languages.
So why did arcade cabinets designated to run in 50Hz regions didn't exhibit the same slower speed as it was the case for consoles running also in 50Hz regions ?
As these, unlike game consoles, do not differ between regions - at least not in game related parts. What differs are transformators and PSUs as they need to cope with the different frequencies and, more important, different voltages. Another part that usually differs are the coin slots/money detectors, as different countries happen to have different coins.
Arcade cabinets are closed system, not intended to be interoperable with other devices, like local TV. Consoles in contrast have to do exactly that, work with a local TV at default setting.
A comparable situation with computer would be the Commodore PET. An all in one solution, much like a game cabinet. Id did not have to bother with 50 half frame per second TV. Again, it was the power supply that had to be changed to work with the various voltages available in Europe at the time.
The equivalent in game consoles would be the Vectrex. Here again it was an all in one unit containing the CRT as well. So when MB sold it in Germany, all they did was replace the 115V transformer with a 220V unit. Nothing else ... well, ofc, warranty sticker and packaging had to be changed as well :))