Such systems are called "player-facing"
I don't know how ubiquitous this terminology is, but it certainly exists. I first came upon it in tremulus (p. 4):
All rolls of the dice are “player-facing,” meaning that all the rolls in the game are done exclusively by the players.
A quick search reveals the term being used in blogposts and forum discussions.
Here's a slightly expanded definition from one such post:
Of all the innovations in roleplaying over the years my favorite is the concept of “player-facing” mechanics. For those unfamiliar with the term, player-facing refers to game elements that require the player to roll dice, react, or make decisions instead of the gamemaster. Most every game out there features a majority of player-facing elements such as attack rolls, skill checks, or saving throws along with several gamemaster-facing elements such as NPC attack rolls and damage rolls.
As the term may not be well-known, perhaps describing such games as having "player-facing rolls" would be better.