Interesting - and long! - thread I happened upon. Here in MN I have not hooked up the snow blower yet - wow, that is unheard of.
So, as a farmer, I run a lot of machines with way more chain issues than that, and they run for 100's of hours a year with little issue. A chain on a slow speed blower cross auger is far different from a high-speed close tolerance situation. What I saw in the video will run longer than your tractor will last. The deal is, you are going to feed gravel and ice and snow lumps into that cross auger and hit it with several shock loads per minute that are worse than the bit of wobble it has.
I see they didn't get it perfect, and if it was originally much worse than this, I understand it's an issue that the manufaturer needs to improve.
That said, the bit of wobble will not be a problem for that application. As you back into hard snow, you will be flexing the cross auger and it won't run true anyhow. As you overload the blower with snow, it will again be flexing in other directions - at some points it will be running smoother with the 'pre-wobble' they put in it.

This is a slow-speed, brute force, type of application, and it looks like they are building to meet the situation, not for perfection where it doesn't matter. If you showed us a timing chain to run a valve train, oh boy would that be a bad deal! For running a slow snowblower cross auger - ain't no big deal really.
However, you have come to hate this snow blower, and it will never, ever, never satisfy you. You will look down upon it, and blame it for every problem you have in life for the entire winter season.
I would suggest you try to return it, even if you lose a bit of shipping or restocking, and buy a different brand from a different company.
You will have happier winter seasons.
No good will come out of you trying to keep this blower, they could re-tool it from all new steel and spend $100,000 lining up every hole and cog of the entire machine, and you still will not be happy with it and find flaws and hate every time you hook it up to the tractor. Just human nature. You've talked yourself into this being a lemon, and 20 years from now, with the original chain and sprockets on it, you'll still be thinking what a lousy deal when you walk by it.....
Walk away from it, and buy something different.
Myself, I bought a snow blower that shelled out it's gearbox in the 2nd year I owned it. Out of warrenty sorta but not quite - one of those deals -, I took it to the dealer, he said he got into a paperwork battle with the manufaturer, they wanted me to fill out a 5 page survey & mail to Canada... Dealer said he can get the gearbox rebuilt local for $150 and I'd be back blowing snow on the farm in 24 hours instead of 2+ weeks hasseling with the paperwork & shipping.
I wrote the check for $150 and was able to feed the cattle the next day, and still have the blower tht I bought in the mid 1980's, only put shear pins and oil and a couple of bolts into it since. I didn't get wound up on the issue, and everything was fine. Local place musta had better gearbox parts that the original manufatuerer, and I have a lot of snow blowing over the years.
Likely the original manufaturer 'owes' me the $150 - but things worked out great, they are bankrupt and no longer around, I still use the blower to feed my cattle. Who got the last laugh?
Hope you find a different machine you like and can get on with life, rather than stuck in some sort of eternal gripe.
--->Paul