Most influential companies in my opinion:
1) Nintendo. - They reinvigorated the gaming market after the giant crash in the 80's with the first Nintendo console, spawning the most popular franchise in gaming history, Mario.
2) Sega. - The Dreamcast was ahead of it's time, first console with built in support for online gaming via the inclusion of a dial-up modem and hence was the first console with DLC for games.
3) Sony. - Although not the first company to have disc-based media for storage, they were certainly the first to make it standard as well as a dual-thumb stick controllers.
4) 3dfx. - The first company to make a 3D graphics accelerator "right" with the 3dfx Voodoo card.
Stupidly powerful for the time... And pushed 3D gaming onto the masses, crushing such competitors as NEC, S3, Matrox, nVidia, ATI, SiS, Rendition, Intel. etc'. - Unfortunately 3dfx hit a stumbling block during the Voodoo 4/5 era and was failing to execute as well as it's competitors ATI and nVidia. - Eventually nVidia bought them out.
5) Microsoft. - These guys may have been one of the most influential companies in the world when it comes to gaming.
Thanks to the Direct X API, game companies no longer had to program for the dozens of different graphics cards directly, increasing compatibility and reducing the complexity game developers had to face by only have to work with a single API on Windows 95.
Plus the original Xbox console would become to popularize such features as DLC and online gaming that Sega had started and failed with the Dreamcast, mainly due to the abundance of broadband.
As for game companies influencing the world of gaming... We only have to take a look at:
1) Id-Software. - They MADE the first-person genre popular with Wolfenstein, Doom and the Quake Franchises, enough said.
2) Valve. - No one can dispute Valve when it comes to making games, Half-Life would go on to influence most First Person shooters after it's release.
Valve then made digital game purchases popular with the Steam platform, originally criticized for being another level of DRM, Steam has gone on to be the most popular choice for gamers on the PC when it comes to digital purchases.
3) Activision Blizzard. - Blizzard, this company can't make a "bad" game, they usually suffer from long development times but always seems to make a game that appeals to the masses, StarCraft would go on to become a national sport in Korea...
World of WarCraft would displace all other MMO's that came before it to become the most popular MMO game in the world.
Activision would go on to spawn the most popular AAA game of all time, Call of Duty with it's yearly releases. - No more needs to be said about Activision.
4) Westwood. - Before being gobbled up by EA, this studio was the grandfather of the RTS genre with Dune and Command & Conquer.
Dune would go on to influence every single RTS including the likes of StarCraft.
Now other companies I could probably add to this, but meh. Apple doesn't even ring a bell with me, I've never owned an Apple product... Never will. They shunned gaming when gaming was just hitting it's stride in the 80's and 90's. It wasn't until Apple released the iPod that they even gained any recognition for being a platform capable of playing games. - There is a reason why Gamers use Windows for gaming on the PC after all and not MacOS.
Facebook could be worthy of mention, they helped push Shareware/Freeware casual games to the mainstream.
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