Yes, that does look like tail biting to me. Unfortunately, it can be a very frustrating and chronic issue with some fish...my own hypothesis is that it is the result of breeding for unnaturally long tails (many seem to bite just to lessen the weight).
My concern is that your tank may not be cycled. Even a filtered tank can build up ammonia quickly (the filter provides a place for beneficial bacteria to colonize and remove waste from the water by metabolism; it does not remove the waste itself). Do you have anything to test the ammonia, nitrite, and nitrate levels? I would make sure the water is ok first, then worry about any other possible causes.
Hope this helps! Also, if you're interested, there is a great article about the nitrogen cycle here: http://www.tropicalfishkeeping.com/f...m-cycle-38617/