First signs: the MSX-Commodore-Amiga era
The first signs of the spread of videogames in Saudi Arabia appeared probably some time around the early 1980s, on the home computer scene in the MSX-Commodore-Amiga era. Videogames were the most popular of all apps for those machines, so naturally electronics and computer importers felt there would be demand for the videogame consoles just starting to get popular in the US and Japan. Most famous of all consoles in the earliest era was of course the Atari 2600. To this day in Arabic slang, the word "Atari" is literally synonymous with "videogame console".
The 2600 was the first console to ever achieve popularity in the Gulf and thus started many on a life long passion for videogaming. It created more demand for games, causing importers who were encouraged by the success of the 2600 to import several consoles like the Intellivision, which was, shall we say, not quite so popular... Video gaming was kept alive throughout the 1980s thanks mainly to the MSX and the 2600. The NES was hardly imported at all, unlike the Famicom, which sold like crazy and by the early to mid-1990s was well recognised.
Gaming Renaissance: the Famicom to 16-Bit era
The Famicom started the golden age of videogames in the Gulf. A torrent of bootlegs from HK and Malaysia as well as other places helped flood the market, cementing its popularity. At one point you could even find Famicom games in some grocery stores!
The Famicom was the console of which some of my earliest and sweetest memories of gaming belongs to. Even now when I hear Adventure Island 2, "Fighting Road" or Star Trek I get the urge to track down and play those games again. Only one console holds a closer place in my heart, the Sega Mega Drive (Genesis).
The Mega Drive was always more popular then the SNES around here and therefore had many more games imported for it. More importantly, by 1995 or so the first Arabic magazine dedicated to gaming news was released and began reviewing import Jaguar, MD, and SNES games. Now there are dozens of Arabic publications dedicated to all things gaming.
Gaming boom: the Saturn-PSX era
Although they've been out for some time, sales of the PSX and the Saturn only caught up with sales of cartridge based consoles around 1996. The Neo Geo CD and the Sega CD were released before them and were also relatively successful, but didn't sell as well as the next generation of CD based consoles, possibly because they did not have a large (if at all) bootleg market to popularize them.
After about 1998, sales of pirate games actually exceeded those of legitimate games. The reason bootlegging boomed with the PSX is because CDs could be copied locally, unlike cartridges which had to be imported, often from places in Asia. You could walk into most videogame stores and ask what games they had and the dealer would put on the table several huge books, which on closer inspection were revealed to be heavy-duty picture albums used as catalogues for several hundred photocopied PSX game covers.
Despite the ever popular bootleg scene, officially manufactured consoles and games were also always available. It should be noted that these statements are based on my POV of the gaming scene in Saudi Arabia but it should also apply to the rest of the Gulf.