Well sorry to bust your bubble on that last point, but that is what the law says. Penile penetration without consent of the vagina, anus or mouth of another is the physical act that constitutes rape.
And yes, you may well have been raped if you had sex while drunk, if you did not consent. Sex without consent is rape.
I do not see why the OP would be any more worried about the prospect of rape than any other interpretation of events. Her DD participated in something she normally does not and the consequences for her are MAP and a visit to get tested for STDs. Rape or no rape, those consequences are distressing and a pita and would be necessary.
An allegation of rape would be almost impossible to prove at this point as there were no witnesses and the recollections of teens who were possibly quite drunk would not make a case that would stand up in court. However, that does not mean a rape did not occur here.
The circumstances as described would make me suspect the idea of sex with this particular boy was not something the DD had planned, and now she doesn't know where their friendship stands. At best it was an ill-advised spur of the moment thing and at worst the boy took advantage of her while she was incapacitated (in other words, maybe he raped her); maybe they were both drunk.
But it would be wise for the OP and her DD to ask whether she feels she gave consent all the same and to discuss the human rights that women have when it comes to sex, especially in light of the fact that many women here on this thread seem unaware of the legal facts concerning rape.
A girl does not have to go along with sleeping arrangements that are surprising or that do not suit her. One thing does not have to necessarily lead to another even once in bed willingly with a boy, without contraception and without the context of a dating relationship, or even with contraception and in a dating relationship, if the girl does not want it to.
If the DD is going to have ONSs freely chosen as part of her sexual experience then she needs to be able to take responsibility for negotiating condom use; how she does this with people on a ONS basis is something she may need coaching about.
The DD also needs a word about drinking and impaired judgement.