I think it might be, Ultima Underworld, Dark Forces, Marathon, many others were story-driven well before Half Life. So I don't think it's story that did it. The console aspect is something several designers have written about, including Romero, I just couldn't google my way back to the references.

I remember one of the biggest praises given to Call of Duty (EDIT: actually, reading further down, I think it was Soldier of Fortune that I was thinking of!)

MOHAA, I think not COD or SoF.