Why do dual N-back games use certain letters? Every implementation of dual n-back that I've ever seen uses the set of letters 'C', 'H', 'K', 'L', 'Q', 'S', 'R' and 'T'.

Why is that?
The set is not always the one you suggest. There are many implementations that don't even involve letters, but use random shapes, numbers, spatial locations, or other stimuli.

In Jaeggi et al., 2007, they used spatial locations for the visual task, and


  The auditory material consisted of eight German consonants (c, g, h, k, p, q, t, and w) spoken in a female voice and selected on the basis of their distinctiveness.


(emphasis mine).

In Takeuchi et al. 2010, they used numbers and locations:


  “Dual” N-back task. In this task, the number stimuli consisted of numbers, 1 to 4, presented in a random sequence in one of four places on a line.