Where is the strategy in this game? Is it the deckbuilding, the playing?
In constructed, I'd argue that deckbuilding is not exactly part of the game. When you play a constructed game, you're not just competing against your opponent's deckbuilding ability, but the deckbuilding abilities of everybody your opponent learned from. As such, constructed games can't test deckbuilding skill.
In constructed, there are three broad categories of skill: selecting a deck, tweaking the deck, and playing the deck. Doing the first two well requires a good understanding of counters and which decks are currently popular, but you can ignore it and still do well on ladder, though maybe not so well in tournaments.
Within playing a deck, some skill activities are: mulliganing (selecting which cards to keep in your opening hand); tactics to find good trades, compute lethal damage, play cards in the optimal order, etc.; guessing which cards your opponent has in hand and may draw; anticipating which cards you may draw; evaluating the game situation and inferring which turn outcome is more favourable to you (for example, whether to push for face damage, and when to save removal). Many of these exist in Dominion too, but they are much more involved in Hearthstone, which is good because it compensates for the loss of in-game deck-building.