No, this doesn't get at the point of end-to-end encryption. Better to look at it in terms of the parties involved -- E2EE implies that there are two or more parties, and that only some of those parties should have unencrypted access.

In the case in point, the parent (camera owner) is one party and Nanit is another party. (Prior to the work in the linked post, AWS S3 was another party). The goal of E2EE is to deny plaintext access to some of these parties. So, in an E2EE deployment, Nanit (and AWS) would not have unencrypted access to the video content, even though they're storing it.

As chrismorgan pointed out, if Nanit did not have access to the unencrypted data, they could not do server-side video processing.

(Also, FWIW, there are multiple clients in this scenario -- the parents' phones are clients, and need unencrypted access to the video stream.)

(As an aside, where I used to work, we did some cool stuff with granting conditional access to certain server-side subsystems, so that the general data flow was all end-to-end encrypted, but customers could allow certain of our processes to be "ends" and have key access. This was really elegant; customers could dial in the level of server-side access that we had, and could see via the key authorization metadata which services had that access.)