Your wife got one X Chromosome from her mother and one from her father. Her half sister also got one from her mother and one from her father.
Their fathers are different so those chromosomes won't have anything in common.
Their mothers are the same, but the X Chromosome is taken from a combination of their mother's parents. It is about 150 cM long and will on average crossover 1.5 times. Of course, it can't crossover 1.5 times but will crossover 0, 1, 2, or 3 and occasionally more, but the average is 1.5 times.
So each half sister may get any part of their maternal X from their mother's mother or their mother's father. There is a 1/2 chance they get the same part. That means that the two half sisters will on average share about half of their X chromosome.
Now we take the son of your wife's half sister. He gets his one X chromosome from his mother. But what he gets is a combination of his mother's mother and his mother's father. His mother's father will not match with your wife. So on average, you would expect 1/4 of his X chromosome to match your wife.
But due to recombination, the chromosome may have had 0 crossovers, and he may have got his entire X from his mother's father. In that case there will be zero match.
Or the chromosome may have had 1 or 2 or more crossovers, and the parts he got from his mother's mother may not have been among the approximately 50% that your wife shares with his mom.
Probability-wise, there may be a 20% chance that this case of no X sharing might happen, and you seem to have encountered this situation.