I love lifting, and I agree with this. Even running outside, though repetitive, causes you to constantly scan the ground ahead of you for obstacles (crack in the cement, puddles, dog poop, etc), you have the stimulus of the moving background, cars/people/stray pets to avoid. You may not have to think hard about theses things, but your mind is always processing and responding to the stimulus.

For me, I think I get the most mental benefits out BJJ. I'd wager any martial art with live sparring would give the same results.

When you're doing live sparring, as opposed to just drills, you have to make constant, near instant, adjustments to your defense, look for offensive openings, scan your rolling partner's movements and try to anticipate their next attack, all while being aware of other trainees on the mats (to avoid a random foot or falling body), and working to slow your breathing and maintain composure.