I believe the reason is that there is no way you could sponsor an adult of the same sex.
A man who is a US citizen can sponsor a woman or a woman as a US citizen can sponsor a man as a fianc?, but I do not think same sex relationships can be sponsored in that manner. And since there is no gay marriage allowed in the DR, you could not sponsor them as a spouse.
That is simply incorrect. An American can sponser them as a fiancee on a fiancee visa-- not easy to get but possible.
Also should the OP fall for a gay guy who HAS a US Visa, they can marry ANYWHERE in the US now. The husband would have to return to the DR and await a visa petition.
http://www.visajourney.com/portals/index.php?country=Dominican+Republic&tpage=1&ppage=5&forum=80
It will cost somewhere near $1000 to just file the application. There must be a ton of supporting evidence that the couple is really a couple. And the OP must have an income over 125% of the poverty level - which is about 20k http://www.immihelp.com/affidavit-of-support/i-864p-poverty-guidelines.html
Anyway - since the OP was just here on a brief vacation and fell for two different guys - I think that a marriage which will pass Embassy standards is a long way off.