That's completely up to the execs at ESPN. If they think it warrants her being fired, then it does. Whether fair or not, unflattering pics and videos that fall under a Google search are used against employees and job applicants all the time. This is especially true for those with an image to uphold (and likely have a moral turpitude clause written into their contract), such as someone that works on television. There was a high school teacher fired in California last year because her husband posted a pic to Facebook of him grabbing her breasts while she was in a bikini and holding a beer. That may not be fair but that is reality. If it's in the public realm, it's up to each employer to decide what is and isn't their business... and fwiw, Britt McHenry was apparently not very popular with her ESPN colleagues even before this video surfaced. None of them have come to her defense and TMZ has posted several comments (unnamed, of course) both from on air talent as well as a high level producer which both say how replaceable she is and that she should and hopefully will be fired.
...and by the way, is she really that attractive or does long bleached blonde hair have a halo effect? She is definitely not an Erin Andrews or Allie Laforce.