Is his father regarded as a martyr if he died on the job?
Undoubtedly the efforts of fathers to earn a living in order to spend on their children and make them independent of means so that they will not have to ask of people is something for which they will be rewarded if they seek reward with Allah for that. Al-Bukhaari (56) narrated from Sa‘d ibn Abi Waqqaas (may Allah be pleased with him) that the Messenger of Allah (blessings and peace of Allah be upon him) said: “Verily, you will never spend anything, seeking thereby the Countenance of Allah, but you will be rewarded for it, even (the food) that you put in your wife’s mouth.”
It was narrated that Abu Hurayrah said: The Messenger of Allah (blessings and peace of Allah be upon him) said: “A dinar that you spend for the sake of Allaah, a dinar that you spend to free a slave, a dinar that you give in charity to a needy person and a dinar that you spend on your family – the greatest of them in reward is the one that you spend on your family.”
Narrated by Muslim (995).
Al-Haafiz Ibn Hajar (may Allah have mercy on him) said: In the hadeeth of Abu Qilaabah from Abu Asma’, from Thawbaan, who attributed it to the Prophet (blessings and peace of Allah be upon him), it says: “The best dinar that a man spends is a dinar that he spends on his dependents, a dinar that he spends on his mount (for jihad) for the sake of Allah, and a dinar that he spends on his companions (in jihad) for the sake of Allah.” Abu Qilaabah said: He started with dependents, and what man will earn a greater reward than a man who spends on his dependents, to preserve their dignity, and Allah benefits them through him?
At-Tabari said: It starts with spending on dependents, which includes one’s own self, because a man’s own self is among his dependents; indeed, it has a greater right over him than the rest of his dependents, because no one can keep others alive by neglecting and destroying himself. Then comes spending on dependents.
End quote from Fath al-Baari, 9/499
For more information, please see the answer to question no. 69960
Based on that, your father died doing a good deed, for which we hope that he had a good end and acceptance with Allah, may He be exalted. But that does not necessarily mean that he was engaged in jihad in the specific sense of fighting the mushrikeen for the sake of Allah.
With regard to jihad in a general sense (which means striving), which includes every act of obedience to Allah, there is no reason not to say that in general terms. But this does not mean that he died as a martyr either, because not everyone who dies doing a righteous deed dies as a martyr.
And Allah knows best.