Yes, you should be able to build it.
There are 3 installation methods - using the makefiles, cmake, and spack.
Looks like you are trying through the makefiles.
In your make.inc you have to have
BACKEND = hip
You can copy one of the examples and modify it as needed, e.g.,
from the main magma directory you can copy one of the examples:
cp make.inc-examples/make.inc.hip-gcc-openblas make.inc
This example is using OpenBLAS on the CPU (MAGMA needs LAPACK for the CPU).
There is also MKL example if you have MKL. After that you can follow the
instructions in README.