Play variant from position (vs the machine)?

In the "analysis board", after clicking the hamburger menu icon there is a "continue from here" option. After choosing "Play with the machine" the "[play] From position" menu opens. However, the computer plays a standard chess game, even though the analysis board was from a variant game and there is an AI for that variant (three check).

Doesn't seem to have been fixed with the last update.

No, it's not implemented. You can keep track of it to get updates to it.