You will call him childish, and he is perfectly fine with this. If he's completely honest, which he rarely is, it doesn't matter to him what you may be thinking when you look at him, because by the end of this conversation he'll be in your head either way. You wouldn't be here if he didn't want to be there in some form, and neither would anything else around you. When he started this, Near wrote his own rules very clearly in white chalk on the black wall of an old bedroom. These were the rules not to be broken, not to be overstepped, listed in writing bigger than what he usually wrote. He didn't commit them to memory, didn't need to, they integrated themselves into his conscious pretty clearly, and he'd change the rules for the next game. For this one, though, he knew exactly how he wished to proceed, and those were the grounds on which he would.
Near has a strange relationship with his comfort zone, completely discounting certain aspects of his life while being overly accountable of others: you, for example, are relevant right now, and he illustrates you into the picture he keeps in his mind, a bird's-eye view of the scenario as far as he knows it. He won't destroy the image of you when he no longer needs it, but simply discard it. If he ever needs you again, he will recreate you, but the fact of the matter is that you are only important for as long as you are important, and once you've left the room you no longer will be.
The toys are there for thinking. He will not tell you this- it doesn't matter if you know or not, and he refuses to explain himself unless it's immediately necessary. The toys are the tools he is most comfortable with, and he will prioritize his comfort and himself over you and under the situation at hand. He looks at his cards with constant shuffling, arranging them in the order that best suits him- not what suits his purposes, but what suits him, purpose will come after and if he must reshuffle then so be it. You may think this bizarre, an open show of vulnerability, from his reasoning- "Well, this is how I like it"- to the very display itself, him below you, sitting while you stand tall, hiding behind a tower of any sort that's struck his fancy. To him, it's a show of power, to make you abide by his rules in his abode, to put himself before you without a single thought of your wishes or desires or opinions. The twitch that crosses your face will not elicit a smirk- a smirk isn't necessary when you're standing right in front of him and it won't be any fun for you to hear it in his voice here, now, at this strand of his web.
Near can play many different games, not needing practice but merely some time to hash out the algorithm, to feel it out until he's good enough to trust his instincts about where next to move. He'll play with you immediately, not because he's competitive but because to him it's a language, he understands his own moves when he sees how they fare against yours, it's a learning experience not a contest. If you want a contest, though, he might give you one, but the reason will be to test his parameters and principles, the rules of the game he'll establish for himself and doesn't care whether or not you play by. Some people call this cheating but Near doesn't see why everyone needs to use the same rules instead of just following their own. The catch is that you only get to pick your own rules once, and if you break them then you're out.