But is there any gay content in his on-screen work?
His first starring role was as someone named Black Dildo in The Ketchup King (2002). I have no idea what that means.
Then he played Flash Thompson in Spider-Man (2002). I walked out after Tobey Maguire made his heterosexist "all stories are about boys and girls" speech.
The evening soap One Tree Hill (2008-2010): he played Owen Morello, a former alcoholic who becomes a bartender and dates lots of women. Nope.
How I Met Your Mother (2006-2012), about a guy taking an interminably long time to tell his kids how he met their mother: he played Brad Morris, who buddies with Marshall, although he dates women. He also says that he was "born a little different," so he may be intersexed. Some queering there.
Then we get to some gay-positive projects:
So NoTorious (2007), about the "real life" Tori Spelling: he played Scott, her crush who turns out to belong to a weird cult. But there's a gay character, Sasan (Zachary Quinto).
True Blood (2010-2013), about modern-day "out" vampires, with Martin Spanjers and Ryan Kwanten: he plays Alcide, head of a werewolf clan, who has sex with women. But there are several gay characters, mostly vampires, and the gay-vampire symbolism is played to the hilt.
So: No gay characters, but lots of gay-positive work.
Maybe his man-mountain physique disqualifies him from gay roles, since gay men are still stereotyped as soft, fragile, delicate, and wispy.