When Loki starts his spiel towards the girl, it was intended for the reader. Loki is saying this to you, so if it reads a little strangely, that may be why.
The girl had curled even deeper into herself so that only her watery eyes were above the mess of blankets. And beneath the blankets, she whispered the words along the broken character who was screaming them.
"Because I...I-I'm the m-monster who parents tell their children about at night?"
She hated seeing people in pain, especially people she understood.
"It all makes sense now, why you favoured Thor all these years."
Another tear slid down her cheek.
"Because no matter how much you claim to love me..."
Something inside her clenched. The truth hurt too much.
"...you could never have a frost giant sitting on the throne of Asgard!"
Loki would never fit in. And neither would she. And that hurt.
Suddenly, her attention shifted from the screen to a small glowing dot suspended in her room. It shifted to a cube, then to a large rectangle, and glowed a deep shade of orange. A moment later, a very tall, very familiar, very broken god stepped into her room. Both of them froze for a moment, and teh coloured portal disappeared.
"Are you...is it really you?"
The voice was so quiet that Loki nearly missed it. The girl crawled out of her bed and silently walked over to the equally quiet man. She stared up at him for a few moments, while Loki wracked his brain, trying to find something to say. Some sort of greeting, a least, and then perhaps transition to what was going on and what Mo-
She hugged him.
The embrace caught him off guard, and he froze.
She kept hugging him anyway.
"I'm sorry."
That quiet voice snapped Loki back into the moment.
"For what? You haven't done anything to hurt me."
"No, but I...I'm sorry for what everyone else has done. I'm sorry no one listens, and no one understands...I mean I...oh never mind."
"You understand me."
She nodded up at him, her soft eyes breaking him apart.
"And I understand you," Loki took a deep breath. "You've been watching my story, and I got to see a bit of yours. And though I didn't see much, I see how deeply you have been hurt, how far you have fallen, you tired you are to try and continue on. How much you...understand me. Which is why I might dare to assume you pore over my life, time and time again. To find some small piece of support of reassurance, to feel safe. To not feel so...alone. I...I'm not quite sure what to say, but I do...understand, that is. I do understand you. Although I'm not quite sure how much good can come from just that."
"It can do a great deal of good. It's a powerful thing, knowing you aren't alone."
Loki gave a gentle smile and hugged the girl back.
"I suppose it can be quite powerful, indeed."
She moved back and added, "It's quite mutual, too."
One tear slipped down the god's smiling face, and he nodded.
The glowing point appeared and grew into another portal.
"I-um...I expect I should be returning now...to my world, I mean. I'm...I-"
Another hug. In the back of his mind, he wondered if anyone, even Frigga, had ever truly wanted this much physical contact with him.
"I understand," she whispered.
Another tear and another smile.
"Thank you," he moved back.
"Remember, please, you aren't alone."
Loki had no words left. He smiled through the tears gathered in his eyes and stepped near the portal. "Neither are you."
The girl gave a genuine smile, "Thank you."
The god stepped through the portal, and her words echoed through his mind.
"Remember, please, you aren't alone."
"You aren't alone."
You aren't alone.