Apparently the repair kit for that car included a new pinch bolt and nut so a cheap alternative for pinch bolt removal could be a BFH.
I agree @ok4450. Than, I have never found those bolts to be frozen enough to need a tool like that. Most of the time threading the nut halfway on and giving the nut a whack with a BFH will do.
Or as @“Rod Knox” suggests …the air hammer.
Yosemite
Funny how after 2 plus pages of replies no one seriously answered Shala’s original question of what is the name of the tool in the video.
There were some very good and insightful replies but many of the answers seems to come down to: Because I don’t know the exact name of that specialty tool. I will tell you how to get around having to buy it.
Keep in mind he is not trying to do that job in the video. He is trying to source that tool for his Uncle, a mechanic who requested him to do so. I assume his mechanic uncle has his reasons for wanting that specific tool.
Just an observation. I am as guilty as anyone of doing this.
I hope Shala got enough info to figue out where to get that tool.
I believe I gave a pretty good answer . . . because I told OP what websites to check out. I know for a fact that ALL of the websites I mentioned by name specifically sell tools for european vehicles. Some of them even sell THE factory tools
Sorry, but I don’t feel guilty of anything
But you go ahead, if it makes you happy 
“I hope Shala got enough info to figure out where to get that tool.”
I believe I did just that 
Have I overlooked the rules for posting replies here? Have I been mistakenly rambling off on tangents counter to forum regulations? Wow. I’ve been a rebel without a cause all my life so I’m glad I haven’t mailed in my renewel check yet.
@nbpt100, technically the name of the tool is “Press”. That will be followed by more descriptive words. So several posters have answered Shala’s question. The full name would be in the FSM (factory service manual) and would most likely be callled “Press, special tool xxxx” where the xxxx would be numbers and letters.
Maybe you did not fully read my post.
“There were some very good and insightful replies…”
It is not about guilt to me. You gave some good and helpful info as I think I did as well. You and some others effectively said …I don’t know but you may solve your problem if you look or ask here.
I just found it interesting how some try to solve the problem they know the answer to while it may not be the problem that is specifically asked. People want to be helpful and that is great.
It is sorta like when a politician, or professor (or whoever) is asked a question they don’t want to or can’t directly answer. They say something like …you are not asking the right question " the question you should be asking is …" and then they go off and talk in detail about that. The given answer may be somewhat helpful, it may be interesting, but it is still not answering the question. Some answers felt like, you don’t need that tool! You question is not the right question. Just use xyz and be done with it. That solves a problem but not his stated problem.
There was a lot of info in here and I hope he got enough to solve his issue.
I am not trying to make anyone feel guilty…you are reading too much in to it if you still feel that. In the spirit of Tom and Ray It is an observation about human nature.
Peace!
I feel you are somewhat critical of the responses that we gave OP
We helped as best we could, and I don’t think that deserves criticism
Do you feel if we can’t EXACTLY answer OP’s question, we shouldn’t give helpful advice, which will point him in the right direction?
Not to pat myself on the back or anything, but it’s possible OP already found the tool he needs for sales, from one of those online vendors I mentioned 
It seems like a waste of money (to me anyway) to consider a tool like that when a small ball peen hammer would do the trick. The pinch bolt in the video wasn’t even rusted or splined.
One of my boxes has an entire large lower drawer full of various type of pullers and presses and I can’t think of one single time in my life that I’ve ever had to use a press of any sort on a lowly pinch bolt.
Hmmm, I thought the replies were pretty good considering the video was in German and most folks found no real need for it anyway. I’m not going to do a personality profile but it does stick out like a sore thumb. Rather I think we’ll just do a full refund of the money spent for the advice.
Not having access to a shop manual but usually the factory shop manuals will list the special tools and their part number in each specific section. That’s so the mechanic can see and order the tools needed. I’d just suggest a visit to an Audi dealer and have a look at a manual for the suspension section, then order that part number from the dealer. I gotta believe though the price is sky high. To me that would be in the $250 range but I could be way off knowing what some of the folks her pay for professional tools. That’s why a BFH is often used.
If one of the experts here has a helpful idea, as long as it is on the topic at hand, seems a good thing if they post it, even if they don’t answer the OP’s exact question. First off, the OP is easily able to sift through the replies of interest and just as easily ignore the others, right? That’s no problem. Second, regulars here are likely interested in the responses of those who’s actually done the job that tool does, but in a different manner. Third, internet users may come to this thread via a search and find information useful to them. For example if you type in “corolla HC emissions” into Google, the first link shown is a thread here on Car Talk about my own Corolla. So b/c that thread is at the top of the list, it providing information users of Google who own Corollas are finding generally useful.