Would we have it the same exact way? Perhaps not.
Would we still be here? We were here before marriage was introduced, why wouldn’t we be here after it were gone?
The greek used marriage as a means to an end to propagate society, but didn’t consider it an emotional bond as much as their bond with their same-sex comrades and occasional partners.
The romans were very similar, and didn’t even consider hetero/homo a dychotomy. Rather, they considered sexuality to be divided in active/passive (which, let’s face it, makes a damn lot more sense. I am not attracted to every woman, and i can be damn sure nobody is attracted to all men. So what’s the point of specifying the odds?).
In short, maybe we wouldn’t have society exactly as we have it today, my money is on a much less neurotic society, but, all in all, it would ultimately be pretty much the same. Afterall, some things don’t change just because you’re allowed to fuck around, and raising your own spawn is a biological imperative.