There's not a lot I can say other than what's (I think) more or less common knowledge in the field: QEC is a practical issue, and so is deeply tied to physical implementation, etc. QC however, as an idea, has power in itself; you can define a Turing-like machine that incorporates notions of quantum mechanics, forming complexity classes that are thought to be disjoint from the classical ones (including probabilistic classical machines) (see ref. [2] in the OP). QEC is, then, any strategy that allows you to implement reliable (QC) resources in practice (think classical redundancy). The fact that you are dealing with quantum resources rather than classical makes it harder than CEC. The problem with current technology is that if you don't have QEC you can't really get to a point (resource-wise) where the classical/quantum class separation is relevant. Achieving this separation is what's called "supremacy" (or "advantage"). You can try to sidestep QEC by building quality (as noiseless as possible) quantum computers.
> From a very amateur perspective, it looked like Gil Kalai was arguing that physical realizations would not be impossible, but work at UIST and Google's "quantum supremacy" result, somehow have proved him wrong ?
Quantum supremacy is debated, and so not something I can reasonably comment on. From the explanation above however, you can see that supremacy is achieved whenever you do something with a QC that cannot be done with a classical computer. The problem is proving that something is 100% provably beyond the scope of a classical computer (people are clever, and so it's often not). However, one thing is to say whether people are achieving quantum supremacy, another is to say whether people are doing quantum computing. For the latter, I would say we definitely are. You can definitely access a quantum computer in the cloud and run routines that can only produce the given outcome if there are quantum effects in play. [1] (Whether or not you could simulate these results classically relates to supremacy, not whether QC is real.)
[1] https://quantum-computing.ibm.com/composer/docs/iqx/guide/en...