The Recruiting Test used has remained largely unchanged since 1943 and funnily enough, the amount of people passing has remained unchanged over the last 60 years, unlike other examinations. Generally the people that score best in Mechanical Comprehension tend to be males aged 25+.
The reasoning, literacy & maths sections on their own do not give a full appraisal of the individuals intellectual capacity to complete Recruit Training. There is no pass/fail mark in this section but it enhances your overall score. There is a direct correlation between low Mechanical Comprehension scores and low (below 10.5) bleep test scoring which has categorically identified that low scores in both indicate a less than 12% likelihood of completing Recruit Training. It isn't a selection pass fail criteria, just an indicator. In short: If you aren't good at mechanical comprehension then you need to be excellent in the bleep test to have a realistic chance of passing training.
It's pure speculation on my part, so definitely not in any way the 100% assured genuine reason, but I'm guessing there are mechanical aspects to weapons cleaning, handling & maintenance, likewise accurate map-reading skills -if you are not good at map reading, you can expect to cover a lot more ground before you reach your RV etc.
The clue is in the title, a few mechancal comprehension examples here. It's to do with levers, pulleys gear trains, tools used for particular purposes, basically the logical conclusion of the outcome of a mechanical operation etc,.