I think it's key to define to yourself what it means to be a blues player. without getting into the old "what is the blues?" conundrum. Obviously Robben Ford and Mississippi John Hurt are pretty drastically different, but there are common threads there. One really important recurring theme when you listen to most great players talking about the Blues, and one you see in the vid you posted of Billy Gibbons, is that most great Blues players have a strong sense of the stylistic history of the form.
So...If you want to play Blues music, listen to Blues music. Dig into the old recordings chronologically. Start with Son House. Then hear what Robert Johnson did with it. What happened when the Blues migrated north to Chicago and changed from a rural acoustic form into an electric urban music. Listen to Elmore James.
It's been a while but I remember this being a great book about the roots of the Blues, and history of the early players.
Next trace the different branches of the Blues. Piedmont Blues, Texas Blues, Jump Blues..What was the impact of the Blues on Jazz and Rock.
I don't think you have to be a historian of the Blues to be a player, but you do need to have a sense of where it came from and what you want to do with it.