I'm (yet) not convinced.

First, the links say that MWI needs a linear quantum theory, and lists therefore the linearity among its predictions. However, linearity is a part of the quantum theory and its mathematical formalism, and nothing specific to MWI. Also, weak non-linearity would be explicable using the language of MWI saying that the different worlds interact a little. I don't see how testing the superposition principle establishes MWI. A very weak evidence at best.

Second, there is a very confused paragraph about quantum gravity, which, apart from linking to itself, states only that MWI requires gravity to be quantised (without supporting argument) and therefore if gravity is successfully quantised, it forms evidence for MWI. However, nobody doubts that gravity has to be quantised somehow, even hardcore Copenhageners.

The most interesting part is that about the reversible measurement done by an artificial intelligence. As I understand it, it supposes that we construct a machine which could perform measurements in reversed direction of time, for which it has to be immune to quantum decoherence. It sounds interesting, but is also suspicious. I see no way how can we get the information into our brains without decoherence. The argument apparently tries to circumvent this objection by postulating an AI, which is reversible and decoherence-immune, but the AI will still face the same problem when trying to tell us the results. In fact, postulating the need of an AI here seems to be only a tool to make the proposed experiment more obscure and difficult to analyse. We will have a "reversible AI", therefore miraculously we will detect differences between Copenhagen and MWI.

However, at least there is a link to Deutsch's article which hopefully explains the experiment in greater detail, so I will read it and edit the comment later.