I wanted to speak to this.
Miniature/ board gaming has moved over the decades from hang out with my friends in college, to guys night out after college, to family game night with a 6 year old. That last of the three was a tough transition that was a result of reality as we all grow older. It has also really changed what I buy and why. Also gone are the sometimes angry competitive rules lawyering to be replaced by warm proud experiences that end with a handshake, “good game”, and " can we play again…please!!!"
Before age 6 most games were very hard to play since he couldn’t read, do basic math, or understand things most adults take for granted like spacial and temporal ralationships. I mostly played the game alone and narrated what was happening as he rolled dice. However that magic breaking point hit between kindergarten and first grade as bare bones addition, subtraction, and phoenetic reading is kicking in…now he and I have had a blast playing games.
That said, I chose Dust Tactics. I already own a fair bit of War Machine, but that is too much for now (or I would be playing for him rather than with him) with all of the measuring, focus spending, range estimation, and detailed stat cards that rely on a lot of reading. I have a slew of other games that I see us playing in a year or three, but not yet.
Dust Tactics has a few things going for it. As mentioned, it uses squares on tiles so while 8 inches still doesn’t make sense to him, 3 squares does. The dice rolling is nice too as it uses special dice that have either a blank or a target icon. So all the rules are built around a simple chart where you compare the type of thing you are shooting with what you are shooting and it gives you a number of dice to roll (then you just count the target icons). It is much simpler than a lot of other games with several sources of numbers, modifiers, target roll number, and the useful underlying concept of probability. It is an elegant streamlined feature that makes the game play fast for adults, but also in my case lets me enjoy it with a 6 year old. Also they have recently released Dust Warfare which is a more traditional miniature game (tape measures, morale, etc), but uses the same mini line. So there is built in growth.
X-wing is great too as all the moves are built into cardboard templates, the dice are symbol or blank, and what few stats there are are in colored numbers. The game could be played in a foreign language pretty easily… Which works since reading is a major hiccup for now. The more we play it, the less I need to help him with. And because it is star wars, he loves it and doesn’t notice that I am asking him questions the whole time to increase his use of site words, basic math, and understanding of spatial orientation.
Heroscape is another great choice. It is out of print so your mileage will vary on that. If interested, I suggest garage sales over eBay. That stuff turns up a lot.
The grandparents are not gamers. Some of them detest games. However, they all love seeing him play games-- especially the part when he tells them how many hits he needs, how he knows Luke moves before Vader, or spouts off words like initiative. =)