I am not a Halo Game aficionado. But I watched a few Game Videos, where the cinematic parts of the games are put together.
That said, I think that what this production does is simply the only way to make a consistent SciFi show for a broader audience and not a pure fan-service.
Its decision to show us the human flesh and bone behind the Helmet, how John thinks and how he feels, how vulnerable he is when not behind his armor, how broken as a human, that is the biggest strength of the show from the first season on, and makes this a good experience. Pablo Schreiber is clearly the right choice for this part. Him always behind the Mask, always in combat, would do the show no good.
The Halo TV series can stand for its own as a beautiful, high-level/high-budget modern Space Opera, with the characters and within the world of Halo.
The show does tell a different story than the games, yes. But that is another advantage. If not, it would be just a cinematic recap.
It is, I give that to the critics, not always consistent and perfect. Season one spent too much time on some side-stories and on the new character Kwan, who is kind of annoying to many of the audience, and seems to be hated. But Kwan seems to have a special purpose in connecting the other characters and a big part of the story arc.
But season two is now focused on converging many threads. It is more densely packed and had a breathtaking episode 4, a bit too slow episode 5, in is again gaining momentum in episode 6.
Some voices here write something like "desecration", or even "heresy", as if Halo were some holy book that has to be worshiped. But it is a game with a story and not an Epos that defines mankinds' culture. Some talented people at a gaming company set it up to make it work for players, and now other talented people do the same for the screen. And they do good.