You are absolutely correct! I fully agree with you, Pete, that Norris was tough. Chuck was at the top of the martial arts 1964-74. You don't win championships without being tough. He was tough in his time and tough historically.
The video you list shows the results of a 1966 fight with Allen Steen, another Karate champion, not the Gracies. Allen Steen beat Chuck Norris for the Karate Championship in 1966. By 1988, Norris was considerably past his prime, but maintaining his image doing movies. Brazilian JiuJitsu got its start in the USA in the early 90s.
Norris also studied wrestling, boxing and judo, but he was not proficient with any aside from Judo.
It should be noted that Chuck Norris is sometimes listed as having been a champion of full-contact karate, something he has never been. He fought points-based karate. At that time, karate matches were point sparring - one hit and they award a point and restart the fight.
Full-contact was created in 1970 and formally adopted in 1974. Norris never competed in full contact matches. At that point he was too involved with his movie career.
His career performance was commendable. His won-loss record was outstanding, something like 180-10.
He did learn some JiuJitsu with the Gracie family. Chuck had the following to say about his first Jiu-Jitsu lessons with the Gracie family:
“I tracked the Gracies down in Rio, and I went to their school. And I met Mr Gracie, the father. I met Rickson Gracie, who was the world champion at that time, and Royce Gracie.
“So I asked if I could work out with them. And they said–very cordial–, ‘Of course.’ And I was a black belt in judo, so I thought I had some pretty good grappling skills. Anyway, I got on the ground with Rickson Gracie, and it was like I’d never had a lesson in my life. He played with me. And then I went and worked out with Royce for a while. And then Mr Gracie said, ‘Chuck, let’s you and I grapple.’
“Mr Gracie’s about this big [gesturing that he is short with his hand]. So we started working out, and I mounted him. And he says, ‘Okay, Chuck, punch me.’ And I said, ‘Mr Gracie, I’m not going to punch you.’ And he said, ‘No, no, no. Punch me.’ So I brought my hand back [to punch him], and that’s the last thing I remember."
Royce Gracie beat many Karate proponents - Minoki Ichihara, a black belt in Karadeto Daido Juku and Kyokushin karate. Ichihara was considered a "living legend" in Tokyo, who had won over 60 full-contact fights. Gracie submitted Judo and Taekwondo black belt Remco Pardoe who outweighed Gracie by some 80 lbs.
There is a video on Youtube of a bout claimed to be Rickson Gracie versus Chuck Norris. Gracie chokes the guy out in 30 seconds. Actually, the video is NOT of Chuck Norris fighting Gracie! Norris was present, but not fighting.
There always will be arguments about how one martial art compares to the next and which is the best. Now, there is no one fighting technique that dominates MMA. The successful fighters are proficient in all of them - boxing, kick boxing, Muai Thai, Brazilian JiuJitsu, wrestling. The one martial art you do not see in the MMA ring very frequently - karate.
Ron