Hi,
we have just checked in your installation and the issue seems to not depend by mobile devices, since we cannot see the compare list even in our PC.
We have also tried it in our local installation and it works fine. So, maybe some plugins you have installed (or your theme) are causing this issue.
Please, try to deactivate all plugins, leaving only WooCommerce and YITH WooCommerce Compare active, and see if the problem is solved. If so, try to activate them again, one by one, to see which one causes the issue.
If the problem isn’t caused by a plugin, try to activate the default theme Twenty Sixteen and see if you have the same issue.
Also, if you have customized some files in your theme, please try with a fresh installation without any customization.
Please try this solution and let us know what’s the result.