No, he is not driving it as fast as it can go, it is a very rare and historic car. Enjoy seeing it driven. I have had the pleasure of being driven in one of these many times as a young man, it may not be fast or quick by the standards of todays sports cars, but the old girl can pick up her skirts if asked!!!!
Most of the Bentley drivers do drive them pretty hard. I've seen Speed Sixes being drifted sideways at Dunsfold. All W.O. Bentleys are so heavily (over-)engineered that it's nigh impossible to break one. Leno has an 8-litre engine and gearbox in a 3-litre chassis, twin-turbocharged to 1200bhp, all stock mechanically apart from the blowers, and it hasn't broken yet...
Also, I was wondering if you were aware that the course is about 8.4 miles long. There is zero power assisted anything on the car, and it weighs about as much as a truck. The cars were notorious for overpowering the tires, and they'd give out well before the cars did. Top end was somewhere between 120 and 140. To get that much weight going that fast, with the stock engines of the day (another point you may have missed)...well, I think he did quite an admirable job.