It is not just that he had no way to approach women. He had no friends either, neither males nor females. He did not talked to anyone except parents and 1-2 friends his mom found him when he was preschooler. (Third refused to associate with him anymore.) And the two treated it as chore. He was profoundly alone, except like minded people on Internet where he had a lot of contact.
And it was like that for years, because he refused to go to school after one day and was learning from home - visiting once in a while for contact with teachers. He socialized on Internet and world of warcraft. Literally.
It is just that. His inability to have girlfriend was extension of him being profoundly alone and profoundly incapable of any relationship.
But, he was not gay. Homosexuals have nothing to do with any of this.
His entire strategy was whining: "Hey, I am so awesome, why don't the attractive girls approach me?!" I don't remember hearing about any specific step he made to approach girls, not even saying "hello". He was just a guy addressing other guys, expecting that he should somehow magically obtain a girlfriend without even trying, insisting that he deserves it.
I strongly suspect he was a gay in denial. Before anyone gets performatively offended, no, this isn't a statement about gays in general, this is a statement about Elliot Roger specifically. Watch the videos to understand what I mean. His only reason to get a girlfriend was to impress other guys. Incels are bitter about not being attractive and not having sex. Elliot Roger was bitter about being so awesome and yet not having any girlfriend; there was never a hint of any sexual desire towards the hypothetical girlfriend or women in general, no hint of any specific activity he would want to do with the hypothetical girlfriend.