You have to remember the history of the sport and of the town.
Football is very much a midwestern game. Though it began in the colleges in the east, football as we know it today and especially professional football began in the industrial midwest -- primarily Eastern Ohio and Western Pennsylvania. After the athletic clubs of the late 1800s, the first professional league was the Ohio League which included teams from Massillon (the Tigers), Canton, Akron, Elyria, Shelby, and Youngstown. Football was born and raised here and in Pennsylvania and western New York, but professional football didn't explode until the '50s and '60s.
Prior to the rise of the NFL in the last 20-25 years as the pre-eminent sporting league across the country, the amount of attachment by a city to its particular sports teams is almost directly related to the popularity of the sport at the time of its rise. The cities of the East coast rose at the same time as professional baseball's profile exploded in the early 20th century and thus people from Boston, New York, and Philadelphia were primarily baseball crazies. St. Louis and Chicago were also major commercial hubs at this time. \
The industrial boom in the 20s and 30's began to build wealth in the midwest. Cleveland was the 5th largest city in the country by the 1920s and the post-war boom of the late 40s and early 50s pumped a lot of money into the city and raised its profile. The rise of football as a professional sport coincides with this post-WWII industrial boom. Baseball was around, sure... but the highest times for places like Cleveland, Pittsburgh, Buffalo, and Green Bay were the late 40's through the mid-late 1960s. In Cleveland's specific case, this also coincides with the dominance of the Browns during Paul Brown's tenure in both the AAFC and the NFL. Basically we get a double shot of football hysteria; the economic rise coincidental with football's rise and the dominance and multiple championships of the Brown era. Ask your parents or grandparents who were around at that time what it was like and their answer should help clarify things.
This is why football endures in Cleveland while other sports -- though certainly loved -- don't quite match up. There's a certain aspect about football being in the DNA of the midwest. Football is, truly, our baby. Without the pioneers in the Ohio League and the Allegheny Athletic Association and others like them, football as we know it would probably not exist. Another aspect is (as others have mentioned) that football is a blue collar sport, appropriately so given it came to fruition in the blue collar towns of the industrial midwest. For us in particular, the rise of football corresponds with a kind of golden age for Cleveland economically and culturally. Added on top is a tradition of dominance that ingrained in the Northeast Ohioans of the time, whether it be us or our parents and grandparents, a love of the sport as emblematic of the greatness of the city and the region.