How is the game a Roguelike?

Only the single player campaign contains roguelike elements. If you decide to carry off a heist with Travis Baker on the team, and he dies during the mission, then you have to start the whole campaign over from the beginning. 

This game is about failing and trying again.

Each run of the single player campaign offers many threats, that can let player fail. Players will learn how to avoid some difficult situation, but still there will be other situations or decision, that will lead to a failure.

Playing the single player campaign builds up the EXP of Baker and raising his Boss Level. This means that more perks, stats and advantages are available to him with new campaign restarts.

The game is also invisibly tracking events and achievements, and throwing new challenges and unfortunate situations at you, to keep the drama high.