I'm usually against reductionism as a "merely partial" or "half-account", or "only good to first order" as usual accounts of the formalism after the Laplacian the sum of second partial derivatives, instead for a more singular and integral analysis, since overall there's for a continuum mechanics and merely-partial accounts simply eventually fail.
Then, about the Euclidean and otherwise a system of the world, then about this "Double Relativity Theory" is again for what are notions of "frame-spaces" and "space-frames", beyond the usual notion of "frames". Then, it's perhaps so that there would be a better word than "spaces" for the the ideas of "spacities", since they're analytical settings' just like "frames" are, with regards to instances in time or as for motion meters/second, and about instances in space or about meters/meters. Then, "frame-spaces" and "space-frames" for "Rahme-Raumen" and "Raume-Rahmen" will do, adding enough words to the language of the theory to encompass the idea that real space-contraction and making for space-contraction-linear and space-contraction-rotational simply have objects their descriptions their representations in the theory.
So, being a realist and an anti-reductionist, then these sorts of terms are cognitively consonant.
Naturally no experiment that doesn't disconfirm the old "Relativity Theory" would disconfirm this "Double Relativity Theory" either, though one may aver that adding an aether would make "absolute space", that though variously being considered by physicists like Einstein as being "in the theory".