I heard it runs using Proton on Linux (because Tamashii and Teocida are both a windows only game). I presume Steam Deck is based on Linux, but I unfortunately don't have a Steam Deck to test it with Proton.
I figured out how to make it work on steam deck
(Do all of this from desktop mode)
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Add Tamashii as a non-steam game
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Right click it and go to properties > compatibility, and enable the checkbox there (a dropdown will appear, the default value is good)
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Go to the built in “discover” store and install “protontricks”
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In protontricks select Tamashii
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From this menu select “select the default wineprefix” then select “install a Windows DLL or component”
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Install d3dcompiler_43
You should now be able to close protontricks and run the full shader version of the exe, even in gaming mode. If this doesn’t work try installing some other d3d components or if worst comes to worst, run the exe from the “D3DXCompile failed” folder, which works flawlessly as long as you also follow step 1 and 2 for it