This seems a reasonable and convincing argument.
However, saying that knowledge is hard in the case of chess seems not quite the situation. It don't believe that any one human being could imagine all possible games. We might want to argue that this is at least possible in principle in the precise sense that we know all the rules of the game. But this is certainly not true in practice. The human brain is not fast enough and big enough for any human to go through all possible games.
Assuming that the laws of nature, analogous here to the rules of chess, are in finite number, maybe it is possible in principle to compute any state of the universe at t + 1 knowing the state of the universe at t. But we don't know the state of the universe at any one time, and so we don't know it at t, and so we cannot infer it at t. So, the limited number of rules doesn't help. The crucial factor here is the size of the universe, and the size of the human brain.
The reasoning above may sound convincing, but it is flawed. Suppose there has been a time t = 0, and suppose that the state of the universe at t = 0 could be expressed as a small set of data, as seems indeed the implication of the theory of the Big Bang. Then, in principle at least, we could know the small set of data describing the universe at t = 0, and then use the equally small set of the laws of nature to predict the state of the universe at any one time after t = 0, in principle.
However, the fact is, we weren't there, and nobody was, presumably, and for good reasons. If the state of the universe at t = 0 was simple, then no human being, and indeed no being with the intelligence of even a snail or a nit, could have been there at t = 0. If a human being had been there at t = 0, then the state of the universe at that point could not possibly be described by a "small set of data". The presence of a human observer at t = 0 would contradict our necessary assumption that the universe was simple at t = 0.
Thus, knowledge is not possible simply because the human brain cannot even know itself, for all sorts of reasons but also because no physically real cognitive system could even in principle represent itself.
This, of course, is no problem since we absolutely don't need that our brain should be able to represent itself completely, nor any other brain for that matter, and not even any substantial part of the universe. What we need is that our brain should help us survive in our environment, and this is obviously the case. Knowledge of the world is a red herring. All we need are beliefs that are reliable enough for us to survive, nothing else.
Unperfect knowledge is not knowledge. Either we possess knowledge or we don't. If we don't, we may instead have beliefs, in which case we need to know our beliefs, and we do or else they wouldn't be beliefs. All we need is that our beliefs about the world be good enough for us to survive. Seems to work so far.