I think the computer games are what really helped get the franchise going internationally. I remember my first contact with the franchise was the first Dawn of War, which I really enjoyed, but I think it was only around the time of Dark Crusade that I got to know more about the actual tabletop/miniature game. Being a filthy south american, the official miniatures were and still are completely out of my monetary reach.

I put a lot of emphasis on that aspect of the computer games driving interest because Warhammer Fantasy never had anything as successful as Dawn of War or Space Marine, at least not before the Total War games (which arrived after Fantasy was ditched). Also, for a number of years, 40k grognards will tell you all about the shitty rules of Xth edition (6, 7, 8, 9, whichever), times during which some competitors started showing up. Two notorious competitors to 40k proper, in being sci-fi, are Infinity and Warpath. Within the niche of board/wargames and miniature skirmishes, they're known, but you'll be hard pressed to find anyone outside that niche to have ever heard of either. Neither has a videogame which "normies" can play and get to know about the respective universes.

1D4chan has a lot of info on GW, including early history