According to the Apple Mac Developer's license, if you want to produce for a Mac, you must build the final product on a Mac using Xcode.
There is no such language in the Apple iOS Developer's license.
In either case, this thread is about a Player service only. You need to be able to build your final iOS project that runs on its own without a Player. These are two different things.
TGC is not offering to create the final iOS product for publication.
I don't know of any service that will build an iOS product using your Apple iOS Developer certificate(s).
So, I think the answer is yes, you still need a Mac (the Mac Mini is a good choice, if you have a monitor, mouse and keyboard to add to it.)
Cheers,
Ancient Lady
AGK Community Tester