For those of us that are using an eGPU with their Apple PC, usually you only need to tick the “prefer external GPU” option on the Finder “get info” window for the app you desire.
That said, blizzard does not always utilize the typical singular binary for their apps. As it turns out, HotS (and SC2 and the Bnet desktop app) are examples of such an app. That is to say, the app you see, is not the actual app that runs. So, in order to get HotS (or SC2) to use your eGPU, you must navigate into the “Versions” folder for the app in question.
As an example, on my Mojave system, I have to go to the following location : /Macintosh HD/Applications/Games/Heroes of the Storm/Versions/Base81700/
This location is the actual app for HotS, not the app in the “Heroes of the Storm” folder.
Also, in order to get into the “Versions” folder, I right clicked on the folder and then clicked on “show package contents”.
Hopefully this helps other users that are stumped by blizzards “methods”.
If you are wondering how I figured this out, I found the answer on the StarCraft 2 forums at the following URL :