Here is a video of how American auctions are often run. The auctioneer will have a special way of talking or patter.
Is this common in other countries or do they do something different?
Here is a video of an auctioneer championship.
A multi million dollar horse auction that includes internet bidding.
You mean something like this?
Actually I did my own research and I found similar auctions talk in Japan, Canada, and Mexico. They showed an auction in Germany but it was different.
When my relatives visited from Denmark they said they had never seen such a thing.
IANANA (I am not a non-American), but I just saw an auction on the British show called “Put Your Money Where Your Mouth Is” on Netflix. The auctioneer was very slow and did not have the type of style displayed in the video links you supplied.
I can’t do a lot of youtube searching due to my location, but classy auctions (for very expensive fine art, sotherby’s, etc) don’t do this, do they?
Well not really. it depends. At very VERY, expensive auctions bidders have special signals, phone bidders, and such and many bids are online which doesnt really go well with “auction talk”. But we are talking in the millions like artwork.
Now I’ve seen it used where items go for the hundreds of thousands like racehorses and expensive cars.
HERE is a auction at Sotheby’s.
Well HERE is a video of a congressman, a former auctioneer himself, on the fllor of the US Congress, explaining the billions of dollars each year sold thru auctions and their importance to the economy. He also used auction talk to explain the national debt.
On the other hand…
Here is an auctioneer that can play guitar, sing and Auction-ate…
RIP SteveI have been at auctions in a couple different countries and never ran across patter overseas. Even in this country it seems more common as estate/yard-sale-ish auctions than the general specialized auction such as say coins or documents. Its done (according to a few auctioneers I know well enough to socialize with) mostly for show and because people have come to expect it.
One funny memory was a friend who does a lot of farm auctions; we were having lunch at this little diner in the middle of nothing and he decided as a joke to order in patter and when the waitress (who was NOT amused) returned he thanked her in the same style. His food ended up in his lap. You gotta know your audience. 
Japan fish auction:
It’s also done at most of the livestock auction barns.
I’m very familiar with livestock auctions in the UK and yes, it is on the border of incomprehensible with the bidders giving only the very slightest “tells” that are often invisible to the layperson. Not sure if that crosses over to other types of UK auctions.
I’ve seen a few UK auctions of cars and of liquidated stock - they’re not quite as constantly babbling as livestock auctions, but they have their moments. I think this is a trait of ‘trade’ type auctions vs ‘art/goods’ type.
I have attended many antique auctions in the Midwest and the fast patter is very distinct to each auctioneer. You get used to their rhythms. When I first started watching high end car auctions on TV I was amused by the slow, dignified asking.
“I have twenty five thousand…shall I say thirty? Thirty? Anyone? I’ll accept twenty five then. You sir? Thank you. Now thirty…”. Now I have grown to appreciate this style on its own merits.
But I miss the “hey bidda, ha bidda twenny five - what are you gonna do with an extra twenny five…hoo baba, who baba, I’ll buy it myself…”
I knew one auctioneer well, he was one of the two largest auctioneers in the US to specialize in Watt Pottery. I had been dueling on an item and when it got high enough I shook my head when he came back to me. Normally this gets you skipped from a round and they only let you back in later.
Pat climbed down the steps, strode all the way back to me, microphone in hand and stopped at my seat. “Now Denny, you know damn well this is the only thing you really came here to buy isn’t it?” My hand shot back up and he ran back to the stage, “Hey bidda, high bidda…” Pat could sell stuff.
Dennis
I’ve seen reverse auctions* in Spanish fish markets that went as quick as the auctioneer could talk. I’ve seen charity auctions which were very sedate, with the auctioneer making sure that a raised hand was an actual bid and not someone wanting to ask a question. It varies on the type of auction, the type of items, the type of audience.
The phrasing for going once, going twice, sold is a la una, a las dos, vendido.
If the auction house is doing its job in promoting the auction and bringing in lots of buyers, I have seen auctions go very well and lots of merchandise sold in a very short time. Like whole farms from the dishes in the kitchen to the tractors and implements. So if you need to clean out grandpas big house and property in one day and get top dollar, an auction is the way to go.
Most Australian livestock (sheep, cattle horses) agents auctions would feature auctioneers with a similar patter.
They are less common with real estate agents in property auctions.