This is a terminal program, so you need to have a terminal emulators installed (or ssh server). Installing requires root, since writing to /data partition, or remounting /sdcard with exec permissions. After installing, the program can be executed by a non-root user.
The simplest way to install is to untar the file under /data subdirectory. Then the file to execute is /data/gap4r4p12/bin/gap.sh. If you select another location, edit this file to point to the the path where GAP is installed. The location must have execute permissions, but symlinks are not necessary. It is safe to ignore the warnings if untarring onto VFAT filesystem. If /data is too crowded, you can move a few subdirectories to another partition and symlink to them, but note that some packages include executable files.
I removed a few packaged that I don't use, and took some work to get working.