no it really doesn't. The story is not complete, the change log says initial release. Plenty of other games that have chapters don't get the completed tag after one chapter is finished. Seems like a bait and switch to me. Plus its been over a year since it's release. At the very least it should be removed from the Featured Games Slider since it doesn't qualify
First of all, tags are added by site's admins, so if you don't agree with the tags given go and report the OP asking them to reconsider their decision or open a ticket.
That said, the story is complete: the MC left his planet and got involved in some serious shit, found out that in fact he just wanted to leave his struggling daily life and in the meantime he also found a connection with the Force, some good friends and a reason to train his gifts and to fight for (also he's no longer a virgin). So the initial step of his story-arch is complete and now we can jump into new adventures, that's basically how every trilogy you could name starts out. Also, not sure how many "chapter one" of 3 hours long of a non-completed game you can find on this forum.
It was the initial release because, you know, it was released in this state. A full, completed game which also happens to be the first one of a series, but independent on its own. So it's first release and also final release of "The Warrior's Heart", but the series is planned and in development, next title coming out sometime this year.
The Featured Games Slider is just staff choice, they vote the games they think that deserve this extra exposure. This one ticked all the boxes to be there in terms of quality and support. If it's still there is simply because the feature
has gone on hiatus for some vague reasons, there are also some other games that wouldn't be elligible right now (What a Legend surpassed long ago the 1k patrons mark, for instance). Again, in case you don't agree with site mods, well, you know the drill
Edit.- It would be nice to know what do you think of the game itself, appart from that rant about the completed tag.