I don't get that either. Honestly I don't think he cares. Only thing that matters is winning.
There's a sense of resentment towards the game that probably stems from him feeling superior intellectually to the rest of the game. He wasn't liked in Cleveland. He would talk to the press back then (he stopped when he came to New England) and he would talk down to the press and be very condescending. And that was back in the 90's when the sports press wasn't tabloid journalism like it is today.
The old story of Parcells ripping into him when they were on the Jets because Belichick called a blitz and it worked doesn't tell the entire story. At the time, Belichick was going to the press behind Parcells' back (major no-no in Parcells world) and would tell them how he was behind all of the play calls that worked and how much of a genius coach he was. What he didn't know is that Parcells would find out about and after that blitz call, Parcells put him in his place in front of the other coaches.
I can understand the frustration with coaches, players and the culture of the league in general. Hell, I think a lot of Belichick's philosophies are pretty archaic and I laugh at teams like the Browns that are supposedly using advanced big data people who don't seem very advanced in analytics to me. But, I certainly wouldn't feel the need to cheat to win.
It reminds of watching
Friday Night Tykes where the Outlaws, by pure luck, happened to get the playcall sheet of their opponent in the final game. They didn't need to cheat to win (and I don't think it helped them) and now the perception of them cheating takes away from the talent and hard work of the kids. And nothing is more devastating than just flat out beating your opponent, fair and square. There's no excuses that can justify that.
And as far as disrespecting the game, I don't think that's the proper tact either. You may vehemently disagree with a lot of the things the game does, but if you have that little respect for the game...find a new game or profession to get into.
YR