NES is generally known as "Family" in this region, probably because the Famicom box has that word on it. Also, it has always been the Famicom here. Only a small percentage of gamers back then had the NES.
Genesis is simply known as "Sega".
The Atari 2600 was also referred to as "Atari".
The MSX was also very popular here, and most people had that before the Famicom took over. The MSX was localized and released here by a Kuwaiti company called "Al-A'alameyya" and it was named as "Sakher" (which means "Rock" in Arabic).
The rest of the systems were known by their actual names, including the Neo-Geo.
And I have never heard of any custom NeoGeo game before.