By all the references I could look up, it was a remake. It's not unheard of that a remake features some of the original cast in new roles, as a form of homage. For instance, Spielberg's War of the Worlds featured both Ann Robinson and Gene Barry (the protagonists in the original WotW) as the grandparents at the end.

It's definitely a remake.

I see it as a remake.

I consider it a remake. However, you could probably come up with some interpretation to make it compatible with being a sequel to the original.

I think McCarthy was playing a new character in this movie, who was one of the first people to discover the invasion and was trying to warn people.

I just watched this movie yesterday and found this discussion interesting as my initial reaction to McCarthy was that he was reprising his character from the 1956 movie (which I have yet to see, I'm ashamed to admit).

Now, if anyone is an authority on this subject, it's the director, Philip Kaufman. As expected, he discusses McCarthy's appearance in his commentary and he says: “I thought that Kevin McCarthy would provide the continuity from the first movie which was 20 years earlier in a small town, and in a sense give the feeling that he had run for 20 years trying to warn people of this ongoing process...”

In the featurette he also explains that the answer to ‘How can I get Kevin into this movie?’ that came to him (apparently when talking to McCarthy himself) was: “Let's just suppose he had left the last movie where he wanted to leave it, which is running out of this small town saying, ‘They're here!’ and let's just suppose that he ran for twenty years trying to spread the word...”

As for the movie itself, in the same featurette he notes: “I don't really look on our version as a remake, because it's really totally different. It goes back to Jack Finney's source but it's really a re-imagining, in a way a variation on a theme. We could explore a little bit more of the characters and what makes a pod and what makes people be not pods, and is that not-podiness worth preserving. And that was sort of what [we] really set out to do.”