Direct Answer to Your Question and What This Answer is About:--
People have certain expectations from what they consider to be video games.
People have certain expectations from what they consider to be training tools about artificial intelligence.
These two do not always align. I'll try to find games that meet both expectations.
" ... In the domain of Artificial Intelligence, it's hard to identify a sort of media which is bridging the gap between expert audience and amateurs who have a need for easy-to-consume information. ...
... Why is it so hard to write edutainment information about Artificial Intelligence? Are some good example available in which complicated subjects are introduced with a low entry barrier? ... " ~ mcRobusta, Opening Poster
That is the area that my answer will focus on.
The issue is that A.I. is a deeply complex field, involving hard mathematics and study. Most resources I could find were mid-tier difficulty and required some background in programming to get into. It is much easier to find video games that teach general programming than it is to find video games about artificial intelligence.
Another significant issue is that if you are effectively learning a skill, this is becomes a training tool rather than a video game that is recreational. Thus walking the line between video game and training tool is extremely tricky. People have certain expectations from what they consider to be video games.
Artificial intelligence is hard. Game design is hard. Combining these two is even harder because they are both hard fields. Complexity can multiply complexity.
I have attempted to mine tools and games that are both valid video games and valid training tools.
Relevant MOOCs (Absolute Beginner):--
Certain MooCs fill in this gap. Other MooCs cover advanced topics or mid-tier topics.
Take a gander through this link below:--
Relevant Video Games (Mid Tier):--
Some video games that are related to A.I., aimed at children:--
This is not precisely about A.I., but I have decided to this MMORPG include due to its interesting nature:--
WarriorJS is another relevant title that is an MMORPG:--
The link below is also worth noting because of its innovative nature and ability to apply A.I. to teach children via VR, but it does not teach about A.I. in its own right:--
Relevant Toys (Mid Tier):--
The children are the future.
" ... More and more kids are learning to code at an early age, so what’s better than playing with coding robots that teach the basics of programming?
Robots are the type of toy that brings children together to play. Mums, dads, brothers and sisters can all have fun playing with cool coding toys.
Like many of the educational toys on the market, robots offer a fun and engaging way to get hands-on with learning. Interactive toys encourage children to get involved, solve problems, and make quick decisions, developing their skills through play. ... "
— "20 Best Coding Toys & Coding Robots for Kids." CodeMom.AI - Coding for Kids & Artificial Intelligence. Web. < http://www.codemom.ai/toys/coding-robots-for-kids/ >.
There is a small list of relevant toys, here:--
Relevant Side Notes and Miscellaneous:--
My background is largely in wargaming (or at least what is left of it), such as titles produced by Matrix Games, Paradox Interactive, or Relic Entertainment. I have written about Company of Heroes 2, elsewhere. I have worked in regular eSports (League of Legends, Dota 2; etc.) as well. I mention this so that it may give you a better understanding of where I am coming from and reveal any biases I have.
I am not a child psychologist or professional educator, at least at the time of writing.
I recommend researching intellectual giftedness, particularly in children: < https://en.wikipedia.org/wiki/Intellectual_giftedness >.
I am a strong supporter of the Finnish education system: < https://en.wikipedia.org/wiki/Education_in_Finland >. I recommend studying this system. This system has been largely lauded by many educational sources (see the Wiki link) as being successful. Talking about this paradigm may help people understand my approach better.
Sources, References, and Further Reading:--