It is possible to restrict a job to either a male or female (or someone of a specific ethnic group, disability status, etc.) but only under very narrow grounds (Genuine Occupational Requirements - GOR) as stated in Schedule 9, Part 1 of the Equality Act 2010.
I don't think this job would fit so the firm IS exposing itself to the risk of a legal challenge by using the pronoun "he," which suggests only men could be appointed to the role. If this were the case, they should have stated that Schedule 9, Part 1 applies, but also have the evidence to back up the fact that the job spec meets those GO requirements.)
It sounds like it's an issue of translation - not doing them any favours. It would be worth an email to the advertisers and/or the firm to point out that they could be open to a legal challenge.