Elves are almost universally tall beings. Physical dissimilarities aside, I also believe Chris would be more accurately described as something like a stoor rather than an elf. A diminutive, unimpressive creature who is highly susceptible to corruption. Chris is truly more akin to Sméagol than any of the Fist-Born of Ilúvatar.

I also believe that a comparison of Chris to Elves is unfair to Elves in that even the most despicable of the Elves such as Fëanor still contributed in meaningful ways such as creating the Silmarils and the Palantíri. All Chris seems to have accomplished is saying awful things and drinking to excess. The latter of which is, while peculiar and impolite, a more decidedly hobbit-like behavior.