This is a dutch kickboxing drill that can be combined with kicks as well. The fathers of Dutch kickboxing went to Japan for a training camp giving by Fujiwari, Kurosaki and Shima (the first man that beat a muay thai champ on full muay thai rules.) to learn most of this stuff, but kept their own outlook and opinion of fighting. This is a drill that you can implement in your training as an alternative to the video posted by the topic starter. It learns you to fight moving backwards (often neglected) and forward instead of fighting stationary. With fighting backwards I mean that you are able to hurt your opponent with punches and kicks while going backwards. Moving while punching also forces you to keep your feet closer together, since you are not able to move fluently with a wide stance (for fluent movement look at the Thailand vs Japan video above and look at the width of their stances). All possible because of magnificant footwork, where the feet are jumping rope width and stance upright.
This drill is possible with kicks as well because of the way kicks are done differently in classic dutch kickboxing: You try not to rotate your body into the kick as you see in most instruction videos. This is because rotating into the kick means you have to rotate back as well which costs you time that you do not have if you want to put punches and kicks together (which is a signature of dutch kickboxing). By not changing your body position too much while kicking, you can directly follow up with punches after a kick as part of a combination. This does not mean that your kicks are less hard because you generate power from your hip instead of turning your body in.
Imagine what happens if Jan Plas (the trainer in the video) sticks his hand out at any point like I mentioned in point 1 of the image that i posted
https://prnt.sc/jtb31g. Brilleman will be harder to hit since he is not lunging in like muay thai guy does in the video. This is an important concept. Now look at the footwork of Brilleman, his feet are always shoulder width or even jumping rope width, ready to step in for the next punch or kick, or block if needed.
When your feet are close, you can utilize stepping in and thus leverage your body weight into the punch/kick with your footwork. When your feet are wide, you can't step in because you are wide already and will fall over. Not to mention being vulnerable to low kicks, inside and outside ( see point 4:
https://prnt.sc/jtb31g ). Being advanced does not mean knowing cool spinning tricks or kicks. But doing the simple things perfectly.
Another take away from this drill is that Brilleman is never taking a break and is always in the position to give the next punch, while being in your face to put the pressure on. He is able to do that because his footwork is not flawed. In contrast to what Brilleman does, you often see guys hitting the pads and taking small breaks by readjusting their balance after a combination (as seen by the clip of muay thai guy). This translates into fighters doing their 1-2-3 combinations (ending with a non-optimal stance on the 3rd action so that a 4th action is not effective) and after that stepping back to get into proper position again.
Try to recognize these moments and try to put the pressure on since they have to readjust their stance into a more balanced position. The classic dutch fighting style is all about always being in a position to deliver a kick, knee or punch. That is what fighting against it makes it so hard, since different styles of stand up are not as straight to the point regarding placing your attack. Think of a roundhouse kick which has a large distance to cover relatively to a straight kick from the hip, as seen in the video of Brilleman vs. Jackson. The latter is must faster.
Finally Brilleman does not get out of breath while doing these things, to the contrary of the video that is posted by advanced muay thai guy. This is because he stays relaxed in his punching throughout the whole exercise. He punches hard but stays relaxed. He could have done this for 10 rounds. Training that way for efficiency is also part of dutch kickboxing. It's not about tiring yourself out, but about having a consistent pace for the first till the last second of the round.
All these things and more are put together in the video above against at that time highly regarded undefeated Howard Jackson that could not get an opponent for 2 years at that time.
https://en.wikipedia.org/wiki/Howard_Jackson_(kickboxer). It is a beautiful display of the classic dutch kickboxing style. Look at the knockdown in the first round how Brilleman utilized the 'doorstap/ literally transated to: stepping through', which is a technique where you punch and switch stance at the same time that is not seen anymore in this day and age. He does it again at 5:53 which result in Jackson going down for the second time. Notice with that combination that he does not have a particular stance (southpaw vs orthodox), but switches as needed. Executing this kind of footwork with with speed and power is something that those dutch guys from the 80s were specialists at. Notice how easy it is to block and take over when having a straightup stance at 5:51, where Brilleman kicks, blocks and takes over to knock his opponent down with the 'doorstap'.