The dati leumi are essentially a type of meshichist (no relation to the Chabad type). I’m not sure they would approve of that title, but it’s works for ease of use.
Avi has explained it before. The two types of moshiach, Rav Kook and 1948 stuff being the first, etc. I’m not endorsing it, but if the question is how they can say it’s not galus when moshiach hasn’t come, you can ask directly/respectfully and Avi K will tell you the official answer.