Same issue here, on launcher version 2.1.2481, I specify the game directory(for version 1.12.2) to be E:\DirtBlock\.minecraft yet the launcher when it launches defaults to %appdata%\.minecraft folder still....rending all the game versions mute except the latest which is 1.13......and 1.12.2 is no where to be found in the game version list.....
EDIT: So I snooped around and it appears, at least according to this answer: https://gaming.stackexchange.com/a/100122 is not possible unless you're happy to start the launcher from a batch/bash file or create a sym link in %appdata%\.minecraft directory to your custom directory; which brings up another question, why do you have a non-functional game directory specifier option if it doesn't work as intended, hm?
Hi @unknown
I've uploaded a youtube video of me reproducing the issue: https://youtu.be/-qZFQBhbOmY