The video is a bit outdated. I wouldn't worry about this race until you're winning post game races with the difficulty at max using similar cars to what the AI is using. There are two reasons for this:
One is practice. You get better overall with any car.
Two: It seems to me the AI gets a tiny bit slower when you win a race on Hard mode and this effect stacks to some degree.
On tuning, you need to tune the car for minimal downforce on hard tires with no assists. Push your HP as high as possible within the PP limit. Through the end of the first rain storm stay on hard, engage the assists as needed during the rain. Once the second rain hits go straight to Wets. Everyone will switch to Wets or Intermediates regardless of what compound they were on, which equals out the amount of grip. Now you have an advantage in power, use it. Remember to turn assists on if you need them.
ABS is essential in this race.
ASM provides some stability but uses the brakes to do so, thus slowing you down.
TCS cuts power to avoid oversteer. Short shifting also does this.
Brake balance can even out tire wear and prevent loss of traction if adjusted correctly.
As for gearing, Tsukuba requires acceleration more than it does top speed. The two areas you should be going the fastest are on the short straight before the second right hand hairpin and about halfway through the long right hander before the finish line. Once you exit the left hand hairpin you should be able to stay on the gas all the way up to the second 180 degree right hander. You will have to slow down or even brake slightly on the final turn. Use the full width of the track at all times and aim to start and finish those faster sections on the extreme left side of the track.