Lot's of people love the Zachtronics family of "crafting" games: Opus Magnum, SpaceChem, Infinifactory, and SHENZHEN I/O.<p>And while Super Smash Bros. Ultimate is on the surface a simple fighting game. Once you unlock all 74 characters, special moves, spirits, etc. It's becomes a mind-bendingly massive combinatorial space!
Factorio, the talos principle, the witness, portal. Intellectually stimulating is a pretty broad net however. I find starcraft 2, rocket league, CIV, CS:GO, sim city, flight sims, racing games (dirt rally), to be all "intellectually stimulating".
Well, most games with decent speedrunning communities end up being more intellectually stimulating if you get involved in that sort of thing. The amount of tech and number of strategies you have to learn to master the likes of Zelda Breath of the Wild at a high level is pretty impressive. Same with everything from Ocarina of Time to Super Mario Odyssey to any Metroid game to whatever else. Heck, if you want the equivalent of a phD in either Super Mario 64 or Paper Mario, then videos by pannenkoek and Stryder7x are fascinating:<p><a href="https://www.youtube.com/user/pannenkoek2012/videos" rel="nofollow">https://www.youtube.com/user/pannenkoek2012/videos</a><p><a href="https://www.youtube.com/channel/UCYDnJiF0_RqSjkjvjRbG1tA/videos" rel="nofollow">https://www.youtube.com/channel/UCYDnJiF0_RqSjkjvjRbG1tA/vid...</a><p>I suspect competitive Pokemon would probably be pretty intellectually stimulating too, if at the level of Smogon or the world championships. There are a crap ton of tactics in that series, and trying to anticipate your opponent's own strategies while countering with your own requires a lot of creativity and thought.
Anything by Zachtronics - Shenzen IO/ Opus Magnum. He also made a challenging cirtcuit building game on Kongregator (flash game) called Konstruktor (spelled with Russian characters).
Starcraft 2 is the gold standard of competitive play. It was chosen as Google AI's next big project for a reason, as it combines the best elements of chess, poker and piano playing.
You'll get more responses if you narrow it down a bit, as there's more than one sort of intellectual stimulation - from military strategy to abstract geometrical reasoning.
Most competitive games if you want to play at the highest level are extremely tactical and thus intellectually engaging.<p>Top players all have top tier mechanics and then it mostly comes down to tactics, the ability to metagame etc.<p>I personally enjoyed Dota in the past, for that reason, although I currently play games with smaller multiplayer sessions.
Shenzen I/O - a very clever electronics based puzzle game<p>Or if youd prefer an existential crisis with your video game try the spectacular NieR Automata
Non-competitive?:<p>Mapgames (Europa Universalis 4, Stellaris)<p>Rougelikes (e.x.: The original Rouge, Tales of Maj'Eyal, Nethack)<p>Zachtronics games as previously mentioned in the thread<p>Competitive?:<p>Dota 2<p>CounterStrike<p>Fighting Games (most)<p>Highly dependent on player count, but Starcraft Brood War and Age of Empires 2
Polytopia is a pretty decent indie strategy mobile game which tests your military strategy, tech development skill, and economical maximization like in the Civilization series, also recommended (for PC and consoles only though).
I'd say Horizon Zero Dawn, it kept me hooked wondering what 'zero dawn' was etc. The game itself isn't really intellectual but thinking about that scenario etc can be.