So I ended up submitting this as a support ticket to Storefront as well and this was the response I got:
"Anonymous checkout in Mobile was never an option. I have no idea how to get that enabled in the Mobile skin. The newer versions available certainly allow it though, with the all-in-one responsive skins instead of the dedicated mobile skin functionality."
So we will have to look at upgrading the skin to a responsive one in order to get the same functionality. Thank you for the answer though!