Ok, firstly, this guy believes that there is a high chance he has a baby on the way. Now, given that the OP used condoms, that is unlikely and I don't understand why he is 90% sure the kid is his but maybe he is bad at Science.
Nevertheless, he believes he might have a baby on the way and actually, he is acting quite admirably. He Isnt being abusive by demanding his paternal rights. From what I have seen he has threatened legal action so he can obtain his legal rights over a child he (probably wrongly) thinks is his. Someone in his position would need a good lawyer and lots of money to petition for paternity and it must be awful for the men who are in that situation and are unable to rectify it.
The OP asked if his behaviour is abusive. No, it isn't whilst he believes he could be the Dad. If he refuses to accept that it's highly unlikely that he is the father and/or refuses to accept the results of a DNA test and continues this, sure, he is nuts. But right now, the OP even confused us about how likely it is that he is the father and seems to be operating as if the chances are 50/50 opposed to the very small chance that it really is and given that him being the father would be a nightmare for her, I would have doubts about anything she says regarding the odds if I were him.