Sure looks like one from the videos. If not fighting then what is it?
Maybe it would fall under a combo of fighter/brawler/card game?
But seriously, it doesn't look that bad, and according to the guide given out for the game, alot of it doesn't seem to fit "exactly like Climax Heroes;" a number of things are changed up in terms of effects and strategy, just similar rules and game resources are used. Though again, I'm basing this off of what I've seen of the games, and with Dragon Knight, that's not much to go on, so far.
Also if you put the actual game music to the clips it comes off looking a whole lot better.
For example, try playing this track (it's the same background music for the Cathedral map in both KRDK and Climax Heroes) in the background while watching the Torque vs. Wrath/Siren scenes from the "Advent Deck Power Gameplay" clip and see what I mean:
[ame="http://www.youtube.com/watch?v=TISw1jBbp5E"]Kiva ~ The Cathedral[/ame]
Also, on the topic of character voices (in which alot of the supposedly "annoying" phrases do actually have Japanese equivalents, as far as I can tell, in Climax Heroes, it's just not as noticeable in a "foreign" language) are there any "context" sensitive lines when two particular Riders square off? For example, when Onyx fights Wing Knight are there any specific intro lines or winning boasts relating specifically to the two?
Here's an example of what I mean in action:
[HIDE][ame="http://www.youtube.com/watch?v=_ad1VKUcNjc"]Kiva vs Ixa[/ame]
[ame="http://www.youtube.com/watch?v=QGRNCtVFhm4"]Den-O vs Zeronos[/ame]
[ame="http://www.youtube.com/watch?v=cAztE5bx9XY"]"Hurry up and become Gatack already!"[/ame]
There was also a clip I remember of the Hopper Brothers fighting TheBee and Mishima took TheBee's role in that context, can't find it now though...[/HIDE]