Try changing the template type from "Infoicon" to "Image, video, or gallery". Infoicons have the following "feature": On mobile web, these templates render only the icon, with no corresponding text nor any other content beyond the image.

@Moviesign I made that change, but mobile still just wants to link to the image. :(

Also I'm realizing the Actions and Upgrade Slots (which are meant to be clickable to go to the page for that action or upgrade type) also just go to the icon on mobile. Crud...

I'll try switching it to an Unknown template type; after enough time has passed to clear my cache, I'll load the page again on my phone.

It's frustrating the mobile is so weirdly different from desktop, and I don't understand the intent behind doing that. This feels like a regression to the old days of making a website compatible with either Internet Explorer or literally any other browser. There's always some snowflake that demands absurd special accommodation, and we all celebrated when IE breathed its last. I don't relish having to battle with mobile's idiosyncrasies and having most useful features unavailable on mobile.

Is this something that will change, or is the intent to have mobile be "special" and difficult forevermore?

It's working for me, so I'm not sure what your problem is. I went to the TIE Reaper page and scrolled down to the nav at the bottom (Viewing Full Site) and clicked on the Play Formats icon and it took me to the Play Formats page.