EDIT: Another interpretation of the statement suggests they take responsibility for the event by proxy of deterring said aircraft which was then targeted by friendly air defences.
EDIT II: Prev. statements by Houthis suggest they had formulated new tactics to tail fighter craft with drones/missiles a while back so probably more likely that had something to do with it.
Ansarollah have historically followed up with evidence of such claims against UAE/Saudi aircraft of the same generation. They definitely have the capability, but no hard evidence yet.
The Houthi's are about to find out why we don't have healthcare, any day now!
Ironically what enabled this was the joint US-UK bombing raid on Sa'ana and Hodeidah port, intended to punish them for a ballistic missile strike on Tel Aviv earlier in the week.