Limited athletic success and for many that results in a lower level of pride in the school are among the biggest drivers but I think another smaller part of the dynamic is that relative proximity to NYC makes a de facto Rutgers bar a bit more difficult to establish. Not saying it couldn't happen or won't happen if athletic success really reaches a high level.
But it doesn't seem like it would have the same "home away from home" demand from RU alums/fans because you can actually just get back "home" to NB in central NJ 30 miles away instead and without too much hassle. That's if you're in the city itself or nearby (but further from NB), say basically north and east of NYC, i.e LI, Westchester, CT). They're not automatically looking for that go-to satellite bar option in the same context as a fan/alum of an out-of-market school might be. So in that sense it's somewhat inversely proportional to distance from the campus and that may be counter-intuitive but combined with the lack of athletic success it seems rational.
Meanwhile most of our alums are closer (and on the same side of river) as the school and campus itself, so they're not likely generating as much demand for an establishment that's centrally located (within the context of the whole metro region), i.e. Manhattan, because the largest concentration of Rutgers fans (as a heat map might depict) is more squarely located over central/northern NJ. This only serves to reinforce why a NYC based bar may be somewhat limited in appeal to the broader alumni base, even as large as the one Rutgers has (either living, or working, or both) in proximity to but also within NYC.
