i think at some point they said her expression was hunted instead of haunted

Only things with intelligence can gain levels (but dragons can’t so there had to be more to it than that)

“Maybe I should run without my headphones in?”

Technically she uses earbuds.

“At least, that’s the only kind of song I download.” -> “At least, those are the only kinds of songs I download.

What if the horses are also capable of levelling?

Horses are around, and without spoilers, they are used for various classes throughout the story, including classes like Drivers.

That being said, even in modern times, horses are expensive animals to keep, especially for good breeds. Not many individuals would have access to them, or the means to raise and keep them. Considering the dangers in Innworld, losing a horse to a goblin ambush or such would not be that uncommon, and would be quite costly.

With the ways skills and classes are gained in Innworld, it makes sense that Runners of various types would become one of the standard means of delivery. Children would be able to get Runner classes much more easily, as there would be no requirements beyond having their own two feet. Horses would be useful, but by the time many Runners had the means to obtain a horse (or similar) they’d probably have skills that would allow them to outpace, or at least keep pace with, a horse.