The film's official novelisation goes into a bit more detail about Mac and Blain's backstory. The very short answer is that both of them share a deep bond, but one of brotherhood of arms, not a sexual attraction.
“Good work, Sergeant,” Schaefer acknowledged curtly, his mind trying
to process a hundred details. Then, suddenly sensitive to the bond
that lay broken between Blain and Mac, he added softly, “I’m sorry,
Bull. It’s never easy. He was a good man.”
“I never had no brother. He was it,” Mac replied simply, almost
matter-of-factly, his lips tightened as if to contain his emotions.