The Ice King and Marceline are nearly the same age. Marceline is a vampire, and The Ice King—formerly Simon Petrikov—wears a magic crown that has extended his life but has driven him mad. In "I Remember You" we see that the two have had a relationship in the past, even if the bumbling Ice King no longer remembers, further enriching his tragic story.
During her stint at AT, Rebecca has always championed episodes that extend the "canon" of Adventure Time, creating deeper interrelationships among the characters, and striking emotional chords that resonate with fans beyond any usual cartoon show. She has definite opinions about Marcy's back story too: who is her mother and why she and Simon know each other. But if they ever become part of the AT story, it will have to be someone else on the staff who carries the torch.
The Omnichord that Rebecca played in the demo actually made its way into the cartoon, and you can see Marceline playing it—it's Rebecca performing on the instrumental track. The art here, with the exception of the title card art are drawings by Rebecca.