There's the crux of your issue. This another Cursed Device™ like my Dell Venue 11 Pro. The official Debian guide confirms it: "The T100 is a mixed mode EFI system (i.e. a 64-bit CPU combined with a 32-bit EFI)"
Zorin, due to its Ubuntu base, has not supported 32bit machines for a while and that includes only being able to install a 64bit grub.
The good news is that if you install a 32bit grub manually or by using another OS, such as the official 32bit version of Linux Mint Debian Edition, then you can install Zorin again after that and it should work - at least, it worked for me, as Zorin just added itself to the existing 32bit grub rather than trying (and failing) to install its own 64bit version.
Alternatively, you may be able to adapt this T100TA-specific Linux Mint guide (not necessary for the 32bit Debian Edition, only their main version which is also a 64bit-only Ubuntu base) to work with Zorin's installation media right out of the gate.
https://forums.linuxmint.com/viewtopic.php?t=417076
Disclaimer: I don't have a T100TA and so cannot test this guide, but it is very recent with a good amount of discussion and positive feedback, it seems.