The big picture you are missing is that the while the Giant are in the biggest market, which they share with the Jets, it is their only TV market. The Cowboys have the Dallas Fort Worth market, the San Antonio market, a significant portion of the Houston market, the Austin market, the Oklahoma City market and dozens of smaller markets which includes part of Arkansas, northern Louisiana and New Mexico. They even have Mexico City which is one of the largest markets in the world and where the NFL is growing.
The Giants are surrounded by teams that have their own fan base. Draw a 500 mile circle around New York and you have what 7-8 teams including both Super Bowl teams and the Steelers? Draw a 500 mile circle around Dallas and you the Houston expansion team. It is a simple question of geography. New York has a much higher population density but they don't really extend much beyond their home TV market while the Cowboys have a foot print that covers most of the south central US. That 500 mile circle still has at a guess about 35 million people and most love football.
New York is the center of many things but football is not one of them. You ask which team would the NFL hate to lose the most? The most valuable team with the widest appeal is the answer and hands down that is the Cowboys. My bias against the Giants has nothing to do with it though I admit it is real. I would have made the exact same argument about any team though it would have been a harder argument to make against the Steelers since they are the only team that comes close but they are still second place.
I go back to my original theory that they picked him because he has a goofy face.