This is truly the topic on semantics. Duelyst is many things. I think in easiest terms it is a CCG with a board element. Specifically, it is played on a grid.
There are many comparators. Duelyst took a lot of the great innovations from Hearthstone, like dusting, arena, single player challenges, limited-time contests and so on.
The game it is the closest neighbour to is very likely Summoner wars, and Mage wars arena as a close second.
Link to summoner wars: https://boardgamegeek.com/boardgame/58281/summoner-wars
Link to Mage wars (arena): https://boardgamegeek.com/boardgame/101721/mage-wars-arena
As you can tell, both of these are boardgames. Duelyst is essentially a fast-paced version of both of these games, with less focus on the board. It is a customizable card game with a grid movement and variable player powers. Just like all of these. The details do differ of course.
I can understand where the comment is coming from that Duelyst is closer to a CCG than both of these. It is collectible unlike either of these, and there is less focus on the board. After Shim’zar, I think they went even further and further away from putting emphasis on the grid. This makes it easier to draw the comparison of this to a regular CCG than say faeria.
Note that many CCGs have a board element. Magic has very limited landscape geometry going on. Star wars decipher divided the board in different locations, be they taverns, space station docking bays or star systems. Middle-earth actually has an entire map where your cards move on as a fellowship. Netrunner has a board of essentially the IT infrastructure of a corporation. All of these games are called CCGs. It’s a very recognizable and broad term, especially because all games in this post are very different to each other. Except duelyst and summoner wars.