Going by the DMG's guidelines on determining CR, the answer would be: sort of, yes.
The short answer is: going by the DMG guidelines on CR, it drops it by two, yes, but it should actually drop from 16 to 14, not from 15 to 13.
The long answer:
The DMG describes a defensive and an offensive challenge rating.
The original Purple Worm with its 247 HP and 18 AC would fall into a defensive challenge rating of 12.
It makes up for it with a very high offensive challenge rating. In a single turn, its damage output (assuming average damage is used and all attacks hit) is 22 (bite) + 21 (acid) + 19 (tail) +42 (poison) = 104. This would put it into an offensive CR of 17, but since its attack modifier is +14 (and thus 4 higher than the recommended +10 for CR 17), it's increased to 19. A large chunk of the damage depends on a DC 19 saving throw, but that's consistent with CR 19, so that doesn't change the result.
So it has an offensive CR of 19 and a defensive CR of 12, which should be averaged out. This results in 15.5, which the DMG (according to its examples) would round up to 16.
If we reduce the HP to 184, that falls into the range for a defensive CR of 8. But since its AC is still 18 (and thus 2 higher than the recommended 16 for CR 8), it's increased to 9.
The offensive CR stays the same, so averaging defensive CR 9 and offensive CR 19, we would get CR 14.
The CR of the original monster would actually be 15.5, which is supposed to be rounded up to 16. But for some reason they decided to round down to 15 instead.
The CR of the smaller version, would be 14. So that's higher than 13, but it's still a 2 decrease from the 16 you expect from the original version, or a 1.5 decrease form the 15.5 if we wouldn't be rounding.
That said, the HP reduction has created an even greater rift between the monster's offensive (19) and defensive (9) challenge rating, making it even more important that the players kill it fast before it manages to output its damage...