The annihilation of Quirrell!Mort (assuming that is what’s happened) isn’t something I can envisage as being part of Quirrell’s plot. So, although the outcome Quirrell was aiming for coming to pass would make it look like he was successful in fact his plot failed and Harry’s plot on his behalf succeeded.
It can be argued that Quirrell manipulation of Harry to ensure Quirrell was seen to win was a strand in Quirrell’s plot. But, his fear of death / destruction of his horcrux was so profound my model of Quirrell wouldn’t perceive himself to have won under these circumstances.
Quirrell was adverse to outright lies, so at this point I think he failed.