All maps have problems with representing distance and space in a 2D form, but this become a little absurd. As an artistic experiment I'd give him a pass except he explicitly said:
"Let's get the geography as well because, with maps, shapes and geography are important. Let's try to make my map better than TfL in every way".
He then absolutely butchers the geography in terms of relative or absolute position, changes the shape of the Thames in weird and unfamiliar ways and makes it hard to reason about distances in many cases (Note: don't try and walk from Richmond to East Putney, as it's a lot further than it looks on that map: about half the distance (4.9mi) from Richmond to Farringdon (10.3mi).
I understand why maps get redesigned into different forms, and generally I love it if you're communicating a new idea about distance, space, or some other data point. But I don't really get what the idea behind this is other than "circles".