I would have thought that the DVLA needs to make it clear. The MTW is homologated as a car in the UK because it is too heavy to be homologated as a trike however in other countries it is homologated as a trike (Italy) or as a motorcycle (USA).
The DVLA regs in the article do not really seem to make any reference to a trike that is not derived from either a motorcycle or from a 4 wheeled vehicle. The MTW has been designed as a trike and is not derived from anything else. I suspect they would take the view that, as it is homologated as a car in the UK, it must comply with the rules for cars.
This document seems to be more of a guide to users rather than the actual regulations. Reading the actual regulations may reveal a ruling specifically for trikes.
One could always request a ruling from the DVLA but perhaps it is best to let sleeping dogs lie.