I have given this yet another go… 
And I can confirm that removing ‘system’ from the algolia discourse username setting and running rake algolia:reindex with a dummy user instead worked without error. 
I shamefully did not spot the bit in the instructions about:
It is recommended that you create a dummy separate user who can only see content you consider to be public, and change this value to their username.
And only matched my settings per this instruction:
Once all of the settings are turned on and populated, the plugin configuration should look like this:
Personally, (and I may be biased ) I think we could maybe make those instructions a little clearer. I would advocate for a section ‘Create your algolia discourse user’ as part of the configuration flow.