The file /usr/lib64/mesa/libGL.so.1 is a link to the executable, /usr/lib64/mesa/libGL.so.1.2.0
I renamed both of them to something else and it made no difference running sigil. I got the same error. Those two files are the only mesa files I have found on the system.
I think I will rename the files again, reboot, and see if that makes any difference. I am posting this now in case the computer does not come back up. Messing around with the graphics drivers on this computer has gotten me in trouble more than once. In one case, I broke it so bad that it wouldn't post the GRUB menu.
It took me a while to figure out how to restore it, so if I don't come back.....