To be psychoactive, capsaicin would need to warp your perceptions, rather than solely induce the sensation of burning pain.
I found additional sources going into the likely pharmacology of this effect:
> Namely, capsaicin and vanillin (and anandamide itself) are all agonists of the TRPV1 receptor, which stimulates production and release of endogenous anandamide. When mixed with N-linoleoylethanolamide and N-oleoylethanolamide from cacao, which inhibit anandamide breakdown, the levels of endogenous anandamide are augmented further. When breakdown of anandamide is inhibited pharmacologically or genetically, anandamide is able to produce a state of intoxication similar to tetrahydrocannabinol in rodents and nonhuman primates
Also, psilocybin is probably still scheduled explicity from before the law was passed.
> Any substance which—
(a) is ordinarily consumed as food, and
(b) does not contain a prohibited ingredient
> In this paragraph—
“food” includes drink;
“prohibited ingredient”, in relation to a substance, means any psychoactive substance—
(a) which is not naturally occurring in the substance, and
(b) the use of which in or on food is not authorised by an EU instrument.
So it sounds like Capsaicin produced naturally in things like hot peppers would be fine. But artificially produced Capsaicin added to food might not be.