Lately, Google has begun penalizing sites for not offering mobile-friendly versions, so I want to use the same photo files and database, but with a installation of the mobile theme in a subdomain and the regular desktop theme in the root domain.

Which files contain path definitions that I will need to edit? I would welcome suggestions.

I will check this out: http://www.zenphoto.org/news/mobiletheme/

OK, so easy, thank you! Just go to the plugins list and enable mobileTheme. Then click on the tiny gear icon by that item which opens another form. In that form, from the dropdown menu, you select the zpmobile theme to be activated when the site is viewed with a phone. I tested it with https://search.google.com/search-console/mobile-friendly and it passed! :-)

Glad you figured it out. That would be the way to go if you are not using any responsive theme (except the jquery-mobile theme none of the official themes are yet – we know…)

I struggled to work out how to get mobileTheme working. Eventually I did. You have to upload mobileTheme.php into zp-core/zp-extensions/mobileTheme where you will find Mobile_Detect.php waiting for it. Hope this prevents someone else pulling their hair out.

You don't have to upload it as it is an still included plugin. Just activate it and define the mobile theme to use. Of course having an responsive theme is better nowadays.

OK, I see that now. Then the real problem is that the text in the green box near the bottom of this page needs updating:

https://www.zenphoto.org/news/mobiletheme/

because it says "This extension is officially supported but not included in the ZenphotoCMS release". I only discovered the plugin from this page and so had no idea that it is now included.

Indeed, thanks, you found a bug in our theme actually ;-) Somehow wrong text sneaked in as this appears on all official plugins for some reason.