A lot of competitive games have uneven playfields. For example, in League of Legends, you have to play a gimpy fake version of your hero forever to unlock the real version.

In practice the high level players who you see on tournaments on Twitch are all playing with all cards (or max level heroes) available. In Magic: The Gathering this costs $xx,xxx (for modern) or $x,xxx (for standard). In League of Legends, this costs an unskippable grind, but you can pay to make the grind shorter. In Hearthstone, this costs about $800.

Notably, some competitive games do not have this property. In DotA, you can play every hero at full power without paying money or doing a forced grind. In Ultra Street Fighter 4, you can play every character at full power after buying the game for $40 or something.

Edit: anyway, the original comment was about "purely intellectual" esports. I think this means "0 execution" esports? Like, turn-based games where whenever you try to do something, you succeed in doing it, or at least succeed with a known probability instead of a probability based on a test of dexterity. So Hearthstone is definitely that, and "but Hearthstone has cards with rarities" is a red herring.