While I was looking through the Lidless Eye Players Guide for a different card, I happened across this passage for Cave-drake, which is listed under the CREATURES / DRAKES section:
CAVE-DRAKE
Cave-drake is one of the most popular creatures in the game. It has a good frequency of play and can be keyed to both Deep Wilderness and Ruins and Lairs. Its ability to target the strikes also makes it very effective for killing off wounded or small characters. You can even assign one strike to a small character as insurance that your opponent gets no trophies out of the attack. Note that Cave-drake is actually a Dragon, not a Drake.
(bold mine)
This passage makes it clear that ICE seemed to embrace the idea that Cave-drake is a Dragon and not a Drake, at least around the time of the Lidless Eye set being released. This passage indicates that ICE intentionally chose not to change Cave-drake to a Drake creature type when The Lidless Eye set was printed.
I then looked up Cave-drake in The Wizards Player Guide and found this:
CAVE-DRAKE
Cave-drake is almost identical to the Ambusher, except its prowess can be increased by Dragon's Desolation (as opposed to Fury of the Iron Crown for Ambusher), and it can be keyed to either double Wilderness or Ruins & Lairs. ......
I did not quote the entire passage from the book, but the relevant part is quoted, namely that ICE meant for Cave-drake to be used with dragon-specific hazard enhancers such as Dragon's Desolation, etc.
The Dragons Players Guide says this in the introduction to the Creatures section:
To go with the four Dragons in METW, there are five more Dragons: Bairanax, Earcaraxe, Itangast, Scatha, and Scorba. There are also fifteen different drakes in METD. While Drakes are not as powerful as Dragons, Drakes can be played in a much wider range of regions and sites - from the sands south of Mordor to the northern wastes and from the great sea in the west to the great plains of the east.
Apparently the authors forgot about Cave-drake being a Dragon when they wrote this. The following sentences describing the differences between Dragons and Drakes certainly would support Cave-drake being a Drake, and not a Dragon. However, despite this, they chose not to change Cave-drake's creature type with the later release of Lidless Eye (and they were aware of it).
It can still be argued that Cave-drake is better off as a Drake than a Dragon, and no doubt it thematically makes more sense (even according to ICE's description above). However, the entirety of my post is meant to clarify ICE intent for those who care.