But when I close the dialogue and right click again, the dialogue reappears. It'd be nice if it didn't, which is what the OP is suggesting. Maybe the extra "No" button isn't necessary, but I wouldn't call it "terrible".

Why are you going to right click again? Do you want the browser's regular right-click context menu? Okay, that's a valid reason. But then what if you want the popup AGAIN after you click "No thanks"? Does the user then have to clear his cache? This is overly complex. If the right-click behavior is being overloaded, then the current solution is better than making it a global preference. Many user will be confused with what "No thanks" means. Are you going to have an explanation saying "If you click "No thanks", then you'll get the browser's regular menu after you right-click from now on? If you get rid of the "No thanks", then you'll have inconsistent behavior. The first time you right-click, something will happen, and something different will happen the second time, and users will be like "WTF?" All this trouble with such a small feature shouldn't happen in the first place. The person who suggested this does indeed sound like a typical PM.

If I want to open Github's homepage in a new tab, I can't use only my mouse (right click -> 'open in a new tab'), I must use Ctrl+click. Why Github force me to do that ? [Edit: middle-click doesn't work for me]

Then this is an argument for NOT overloading the right-click behavior, not for adding a "No thanks" preference. Then all users who want to right-click have to go through ONE EXTRA STEP just to be able to do that?

I think the idea is that you would only have to do that extra step once, have that preference saved, and after that all right click / middle clickers would have the functionality they wanted. Doesn't seem too inconvenient to me, honestly.