"The first move only is orthodox."
What would that mean, do the rules change after the first move?
If a fairy condition allows captureless moves then it's good to see them during the play. A relation between capturing and captureless moves makes some condition well used. Of course, there can be a condition "Only-capturing Chess", that would perhaps be rather boring, just as the lack of captureless move in T&M.

A fairy condition is a self-consistent system with specifically defined movement of the pieces. "Thematic moves" present some THEME, irrelevantly to someone's missconcept of "specific moves". T&M is not a theme and the specific captures are not thematic just because they are specific. Looking from the "T&M system", the captures in orthodox chess appeare as specific, so what, should we consider only the capturing moves in orthodox chess as thematic?
Pierre's selfblock in B1 is trivial but thematic, W1&B2 are thematic sacrifices for a trivial transfer of bK and W2 is a brutal thematic annihilation of a mate-guarding black piece. However, the trivial and brutal motivations for the play are beautifully and skilfully arranged to unite the cycles of Zilahi and of the white captures. Captures are thematic because of their specific motivations for the play and for the cycles, not because of their T&M specificness.