Kinnersley–West–Zamani 3/5-conjecture for the domination game

Let $G$ be an isolate-free graph of order $n$, and let $\gamma_g(G)$ denote the game domination number, the number of vertices selected when Dominator starts and both players play optimally. Kinnersley–West–Zamani's 3/5-conjecture. One should have

$$\gamma_g(G) \leq \frac{3}{5}n.$$

The source mentions this as a central conjecture for the ordinary domination game, posed by Kinnersley, West and Zamani; the supplied text gives no resolution status.