Kinect is out of warranty while i bought it yesterday on amazon

Seeing as it was sold by a 3rd party / marketplace seller on Amazon, I would assume any warranty would be with that seller only... if any at all.

I would review with the retailer it was purchased from.
The Xbox One Warranty, which covers details of accessories, specifically under "Definitions" states that it must be from an authorized retailer. Verify where you purchased it is an authorized retailer, and if not, I would work with them for additional
coverage or returns. If they are an authorized retailer, then they should ensure that they sold you a new product, if they so stated.

Maybe it's because microsoft discontinued kinect production?

microsoft takes into account the factory output of the device. talk to microsoft technical support providing proof of purchase. in toas ways the seller is the one who gives the guarantee in a subsidized way

So from that image I'd recommend you reach out to Infinity Games to verify if they are an authorized re-seller. The image shows that it is sold by Infinity Games, but that's Amazon for you. It is a product made by Microsoft, but is sold by someone else.
Reach out to them and see if they cover the warranty and see what you need to do.