Acidity of hydrochloric acid in acetic acid
So basically I am asking, is this value totally wrong or is it actually quite reasonable?


It's quite reasonable. Compare to page 32 of this reference.


  This was much higher than I expected. Also doesn't this imply that
  Cl− is stronger as a base than HCl is as an acid in acetic acid, which doesn't sound right. 


To answer whether Cl- is a stronger base than HCl is an acid, you need to know the self-dissociation constant of acetic acid, the equivalent of Kw for water. It is about $10^{-10}$. So whereas the middle of the pH scale is thought of as 7, the middle for acetic acid would be 5. So, yes, Cl- is a stronger base than HCl is an acid in acetic acid.