If I understand this correctly, I disagree. Modern philosophical platonism means different things by 'abstract' than Tegmark's platonism. In philosophical platonism, I accept your definition that something is abstract if it is causally inert and non-spatiotemporal. For Tegmark, this doesn't really make sense though, since the universe is causal in the same sense that a mathematical model of a dynamical system is causal, and it is spatiotemporal in the same sense that the mathematical concept of Minkowski spacetime is spatiotemporal, since the universe is just (approximately) a dynamical system on (approximately) Minkowski spacetime. The usual definition of an abstract object implies that physical, spatiotemporal objects are not abstract, which contradicts the MUH. I don't think we really have a precise definition of abstract object that makes sense in Tegmark's platonism, since something like 'mathematical structure' is obviously imprecise.