I would hope that the OP isn't asking for all emails to be stopped, just the especially stupid ones.
And, the T&Cs of Rewards Network say you must be receiving emails from them to (a) earn at anything but the very lowest level (1 mile/$?) or (b) to participate in any promos. A high price to pay for avoiding annoying emails!
If your email program supports it (Outlook does, but many web-based emails don't seem to), you can set rules to automatically delete emails about "new restaurants in your area" and "haven't you forgotten something?" (the new incessant emails "reminding" you to review restaurants), while letting other emails from the same sender show up normally.