Peter Parker was the center of Gwen Stacy's universe. He might as well have hung the moon and all the stars and planets and satellites and clouds and birds Santa's Sleigh and whatever else was up in the sky. He was her bestest friend in the whole world and they did everything together. It didn't get much better than that. She knew there was something different here; he was older, he didn't have glasses, but he was Peter! Nothing could make that anything other than totally awesome.
If the excitement in her voice didn't make it obvious she was happy to see him, then surely the tight hug would. Gwen was too young to really comprehend what was going on in this place, that there were other versions of people she knew. All she could see was right in front of her and that was Peter Parker.
"You really are!" She said, just as excitedly as she had when she realized he was who he was. "And I'm like you! We can stick to things and climb together!" Because that would've been terrible, if her best friend couldn't do all the things she could do. "C'mon, Peter! Let's go play!"