You really think Skyrim belongs there? I’d agree that Elder Scrolls deserves a place, but what did Skyrim do that wasn’t done by Oblivion or even Morrowind?
Source was not an internal engine, it was an openly available engine used by numerous non-Valve games (The Ship, Garrys Mod, Titanfall, Dear Esther, etc etc).
If influential means influencing game design / the industry, inspiring other creators by demonstrating novel ideas, I’d probably have to say Doom or Half-Life. Doom really showed what an FPS could be and kicked off such a dominant genre. Half-Life introduced immersive storytelling that greatly influenced FPS and non-FPS games.