I found out that "Rufus", which I always use for everything related to burning bootable USBs, is burning EFI systems wrong (or at least, burning Antergos image wrong). I used "USBWriter" from Arch wiki and it burned correctly. Now I booted EFI live system correctly (previously I had to switch my system bootloader to legacy mode to boot it).
Then when I installed Antergos on the desired drive. I had to chroot into the newly created system and reinstall Grub2 from there.
For steps used, I've combined both this and this tutorials to achieve the desired results.
mount commands from the second tutorial and
grub-install commands from the first one.
It took two (almost) full days to figure it out, mostly because I used the wrong tool, Rufus, for this particular job. But hey, that's why I installed Antergos, to learn. Now I know "chrooting".
Just made a written note with the exact commands, here they are:
Boot into a Live CD of Antergos and do this:
mount -t efivarfs efivarfs /sys/firmware/efi/efivars
mount /dev/sda$ /mnt
(mount root on mnt)
mount /dev/sda1 /mnt/boot
(mount ESP on /mnt/boot)
mount -t proc proc /mnt/proc
mount -t sysfs sys /mnt/sys
mount -o bind /dev /mnt/dev
mount -t devpts pts /mnt/dev/pts/
chroot /mnt /bin/bash
grub-install --target=x86_64-efi --efi-directory=/boot --bootloader-id=grub_uefi --recheck
grub-mkconfig -o /boot/grub/grub.cfg