Because e is male so he only has 1 x chromosome, and you know that he must has the diseased allele, from his pedigree branch, you know that he must be a carrier. If it were x-linked, he must be affected.
The 1/2 rule is not foolproof; it's just a way to quickly arrive at the most likely answer. You still have to ascertain it by further analysis.
For this question, x-linked seems like the most likely but you cannot rule out autosomal. Further analysis crosses out x-linked.
The trick to answer these kind of question is not asking yourself "why A" but "why NOT A."