These machines should in fact have a 15 year warranty on the transmission, labour only.
You'll probably need a proof of purchase and have an authorised SQ technician do the work, but that's the same for any warranty work from any brand really.
A transmission replacement is a sizeable job on these since you have to pull out basically everything.
It includes pulling out the drum and probably tub as the transmission repair kit contains new seals for the shafts - implying that SQ service procedure requires new seals when replacing the transmission.
That sound in the video could be a lot - but if does not spin at all, with that noise level, I wouldn't be surprised if it is the transmission.
Given the transmission kit is almost 700$ from SQ directly 1000$ isn't an out there quote.
However, if SQ would cover the parts, getting a 500$ quote max is more realistic.
Which is still a very steep repair.
Many on here touted these as living 25 years without a repair - and I always doubted that.
10 years of heavy use seems reasonable to have to do a repair on the machine.
On some other comments:
There is no timer based SQ machine anymore - neither commercial nor for home use that I am aware off.
A bearing replacement would be probably the same level of skill needed.
I just read that they quoted you another lip seal kit - that is definitely redundant, the transmission kit includes everything you need for the transmission repair, even including the 3M sealant.
Run away from what ever tech quoted you that, if he can't look at a picture and google for 2min he's not worth a damn or trying to rip you off.
This is from SQs own website, page 40/41 clearly states the transmission kit already includes the hub and lip seal kit: