According to Triple H himself, before the marriage storyline, he and Stephanie had never even spoken to each other. By the time they did that storyline, Triple H was already a 2 time WWF Champion. When Vince brought him in initially, Triple H was given vignettes and was built up as being a future big star in the company. He became friends with Shawn Michaels, Kevin Nash, and Scott Hall, who had as much backstage power as anybody in the WWF at the time. After the MSG incident, Triple H thought he'd be fired, but Vince only made him get squashed by Ultimate Warrior at WM 12 and postpone his KOTR win from 1996 to 1997.
When they introduced the WHC in 2002, they gave it to Triple H because he was the most established name on Raw and the biggest draw. They gave it to him so that people would perceive it as being on the same level as the WWE Title, if not even more prestigious. They almost gave it to RVD, but the creative team thought that because RVD had never held a world title, people would think that the WHC wasn't as prestigious as the WWE wanted it to be. By Triple H and Shawn Michaels being the first two World Heavyweight Champions, it made the title look valuable and desirable. Triple H's 9 month reign in 2003 (the longest of his career) made the WHC the most prestigious championship in the WWE.
Even after Triple H and Stephanie got married, Triple H has only had 4 world title reigns, and hasn't held a title of any kind for more than 1 night since WM 21 in 2005. By Triple H losing to Chris Benoit, Batista, John Cena, and Randy Orton, it made all those guys look like deserving world champions.
Sure, Triple H might have had 3 or 4 fewer reigns as world champion, but he was always one of Vince's favorites. He's been with the company since 1995, and has worked his way up through the midcard and earned his main event spot. He has had classic matches with Goldust, Mick Foley, Undertaker, Steve Austin, The Rock, Owen Hart, Shawn Michaels, Ric Flair, Chris Benoit, Chris Jericho, Batista, John Cena, Randy Orton, and Edge. Even if Triple H never married Stephanie McMahon (or even dated her), he would still be The Game because he is that damn good.