It is possible for a drunk male to rape a sober female. Or sober male, for that matter.
Where sobriety/inebriation or other impairment comes into play is when the act is predicated on the fact that the impaired individual is unable to consent or to effectively advocate for him/herself or to escape the situation.
A and B are at a party where A has been drinking heavily and B has not imbibed or is unimpaired. B wishes to have sex with A. A is unable to effectively say no, or to escape the situation. B has sex with A. B has just raped A.
C and D are at a party and C has been drinking heavily while D has not. C wishes to have sex with D. D does not wish to have sex. C forces D to have sex. C has raped D, despite C being inebriated.
The underlined statements logically contradict each other. Wishing to have sex with someone is nothing but another way of saying that one consents to sex with someone. According to the entire premise of "too drunk to consent" as stated in your first underlined premise, Person C cannot wish to or consent to have sex with person D, due to being intoxicated. IOW, any sexual act while intoxicated in not a willful one, thus cannot possibly be rape by that person.
This is the inherent absurdity that follows from the first premise, which ignores actual desire, will, and all actions and words conveying such, and instead deems all that irrelevant if the person is intoxicated. By the "too drunk to consent" logic, sex between a drunk and a non-consenting sober person is always sex between two non-consenting persons, and thus not rape by anyone.