No, there is no sexual relationship involved in bromancy , it is a form of homosocial intimacy.
It is a slang formed by combining the 2 words ( brother + romance).
Since it is more common for girls to be intimate in their friendship, the phenomena of guys sticking together intimately seems like a less common thing and was thus coined as a slang term.
Since they are not gays,there had to be a certain term to specify their unique relationship, that is not a typical form of male acquaintance in the traditional sense.
There is another term following the prior :sromance or sisromance, referring to girlfriends of the bromance couple, who compare notes and learn they have much more in common than they ever thought.