Firstly, someone who looks haggard has an exhausted, worn-out, untidy appearance and has noticeably poor health and bad hygiene. This could be a result of someone who drives himself or herself to work too hard, or someone under great emotional stress, fatigue, anxiety or worry, and ends up neglecting personal grooming (untidy, scruffy hair being such an example). Hence, someone appears much older than he/she really is (i.e. showing age). So, I would say that the clue is correct.
Untidy hair, scruffy hair, unshaven face, dark eye rings and bloodshot eyes are examples of what someone looking haggard will present to others. So, your friend clued you in with examples of haggard appearances.
P.s. I am not so sure about [fat around the chin] from your textbook though. There might be a lot of reasons for that: a sedentary lifestyle, excess calorie intake, binge eating and so on. Instead, my attention is drawn to your phrase "works incredibly hard". He probably puts himself in overdrive, paying little attention to his body's needs and personal grooming, thus looking aged and haggard.
I hope this helps.