Rin does things on a whim and this is no different. It is a simply action but it conveys his feelings accurately. If he could he would hug her every chance he had but he's is too afraid sometimes. He knows he's a demon and that she is simply human, but when he wraps his arms around her, none of that matters. He holds her gently because he doesn't want to crush her and he holds her so close, as if she'll disappear. He doesn't even blush, doesn't even think, when he does anymore because too much has happened to care about being embarrassed and he's never been one to think about things anyway.
Shiemi is different though, she still blushes when he hugs her like this. She's so small in his arms, so close, so warm, and she is so much more. When he hugs her it's as if he'll never see her again and he never wants to let go. Sometimes when their alone, he hugs her so tightly he's afraid that one day he'll crush her. She doesn't complain though, because she understands—she always understands. He knows she understand because she holds him just as tightly and just as close. She wraps her arms around him, buries her red face into his chest, and that's when he knows that neither will ever let go. It is in that moment, in that hug, that he knows that their feelings are one and the same.
It is a simple action but it conveys their feelings perfectly.