Interesting. Looks like something I might enjoy a lot, but I wish there was a demo to see how it actually plays.

I disagree. No oxymoron here. There are a bunch of truly fast-paced turn-based games (Shogun Showdown, for example...) Whether this game fits into that description, that's another story...

Something cannot be fast-paced and turn-based.

What if there's a short time limit in which to take your turn (not that I would like that)?

Generally, but not always. Things like speed chess exist. Basically what Breja said.

I agree! Some games, even slightly old, go as far as having more than one gameplay loop/way of solving turns, so they have a slow turn mode and a fast turn mode

However I find this game's graphics too minimal, I hoped it to be more immersive..

If there's a time limit, it's not actually turn-based to me. You've made it real-time.

(It's also likely going to be trash.)

No offense, but that's clearly nonsense. Real time is not "quickly played turns". No matter what time limit you'd put on a turn in Heroes of Might and Magic, you won't turn it into Warcraft.

Once a clock is involved, real time applies. Unless you can stop the timer and actually make it proper turns to take your time. (I accept "real-time with pause" games.) If the timer auto-passes, it becomes realtime.

And, yes, a RTS is a game with rapidly passing, auto-ending and resolving "turns".

Uhm... no. In a real time game, there are no turns. And when the players take turns, by definition, it's turn based, not real time. Yes, in video games there are egde cases that like you describe that try to merge the two. But that doesn't change the fact that in real time a cavalry charge doesn't stop in the middle of the field for everyone else to make their move, and the fact the player only had X amount of time to decide where to send the cavalry doesn't change that.

None of this changes that "fast-paced" and "turn-based" are logically inconsistent. Pick one.

But that just isn't true. Unless you also think that no book can be slow or fast-paced (because it's all page-turn-based), and no movie can be fast-paced (same amount of frames per second)?

The pacing can refer to different things. It can indeed refer to a required reaction speed from the player, which would as you wrote be entirely inconsistent with turn-based play. But it can also refer to story progression. How long battles last. How substantial is the difference between turns.
Different aspects can have different pacing, and different meaning of what pace means.