Any text editor (vi, gedit, nedit, kwrite and so on) can open/view the config.log file.
You need to have the path to where gcc is in you $PATH, it seems your user path does not. So yes it would be better to do this as root (or equivalent) in this case.
FYI: you should build the package as an rpm file so it can be maintained in the database, download the src.rpm file;
As root type; rpmbuild --rebuild --recompile hplip-1.6.7-3.src.rpm
After abit you will see something like (if you have all of the required packages installed);
You do not need to install the debuginfo rpm and it is OK to delete. To install the three other packages all at once as root type something like;
cd /usr/src/redhat/RPMS/x86_64 ;(your location may be different please adjust)
rpm -Uvh hpijs*.rpm libsane*.rpm hplip*.rpm