The game. As played. On the field. As in the actual game of football. Is your reading comprehension really that poor? Even Matt Walsh himself said the Patriots, in no way whatsoever, used the tapes he made to effect the game played on the field.
Only Belichick can say, for sure, exactly why he wanted those tapes, but based on what everyone pretty much considers common knowledge about Belichick, I think it's reasonable to conclude that he wanted those tapes because he is extremely competitive, and is quite willing to do anything he can in order to gain a competitive advantage over the teams he faces each Sunday. I'm sure he'd tape the other team arriving in the parking lot if he thought it would help him win on Sunday. I think it's reasonable to assume that Belichick has complete dossiers of information on every team in the NFL, as does every single coach in the NFL, and he---along with every other coach in the NFL--is continually updating and improving those dossiers in order to give his team---and their team---every possible advantage.
And guess what, "Einstein," all this off-field information gathering means absolutely nothing if the players do not execute on the field. Therein lies the difference between "cheating" and what you conflate to "cheating": cheating on the field has a material effect on the game of football. Rule breaking on the order of what the Patriots did does not. You can't seem to wrap your empty head around the fact that had the Patriots simply moved the camera to the stands, and done exactly the same thing they did otherwise, what they did would not have even been against the rules. The entire essence of "spygate" is nothing more than camera location.
Were the Patriots arrogant to continue taping from the sidelines when they knew it was wrong to do so? Sure. So what? They were penalized for their arrogance, and they took their medicine.
Only those with an axe to grind, i.e., you, and those who are absolutely insane, i.e., Arlen Specter, think this is anything other than what I've just described.
Is your loyalty really that blind? There's a wealth of information available for you to get up to speed on the subject if you had the gonads to accept the truth.