The rabies virus is shed in saliva. More than 99% of all rabies cases (of which there are about 50,000 a year) are due to the transmission of the virus from the saliva of an infected animal/human into the bloodstream of another human.
The website linked mentions “it has been reported” that rabies can be transmitted via intercourse, but doesn’t cite any papers that state as such. Likely the only way this could work is if a human with rabies performs oral sex on another person, creates micro-abrasions on the genital tissue of their partner while shedding the virus in their saliva which infects the 2nd person.
So while it might be technically possible, rabies doesn’t meet the criteria of what we typically refer to as STDs or STIs with our current knowledge and understanding of the disease.