Young adult lit generally features YA characters, and The Demon's Lexicon is no exception. With a sixteen-year-old protagonist, Nick Ryves, as well as his brother Alan (age nineteen), and their new best friends Mae (age seventeen) and Jamie (age sixteen), The Demon's Lexicon is YA-packed. But that's not the only thing that makes it YA Lit.
It also has a focus on characters who are trying to navigate the path from adolescence to adulthood (while simultaneously fighting demons and dealing with magic—those are the bits that make it fantasy), and it features distinctive teen voices as well as teen-centered dialogue and issues.
As for what makes it Gothic fiction, the list is long. We have:
mysterious houses with secret pasts (or presents);
an overall sense of foreboding;
one or more tyrannical romances; and
the sounds of footsteps, screams, or other ghostly sounds.