halacha theory - Is the blood of a non-Kosher animal forbidden because of וכל דם לא תאכלו

Inspired by a recent chat discussion related to this question.

Does the prohibition of וכל דם לא תאכלו - not eating blood - apply to non-Kosher animals? The Rambam writes:

ודבר מפורש בתורה שאינו חייב אלא על דם בהמה חיה ועוף בלבד, בין טמאים בין טהורים

It is explicitly in the Torah that the prohibition is on animal and bird blood only, whether Kosher or non-Kosher

On the other hand he continues:

ודם חגבים ודגים טמאים, אסור--משום שהוא תמצית גופן, כחלב בהמה טמאה

The blood of locust and fish which aren't Kosher is forbidden - because it is part of their body, like fat of a non-Kosher animal

So the blood of non-kosher animals and birds would be forbidden based on the species prohibition, even without the blood prohibition. Is their blood actually a prohibition separate from their species prohibition?

The answer for the Rambam is likely* yes, but I would be interested in the range of opinion in other Rishonim as well.

_{* Because I have seen more difficult readings of other Rambam's that would push the language further than reading otherwise into this particular one, but there would have to be an otherwise compelling reason to do so.}