Assalaamu alaykum. The Prophet, sallallaahu 'alayhi wa sallam, said: “Any action which is void of the remembrance of Allaah, The Exalted, is futile, except for four actions: walking between two targets (ie. practicing with a bow an arrow/spear), training one’s horse, playing with your wife, and learning how to swim [Sunan An-Nasaa’i, hadith 8940 and Tabaraani, hadith 1785] Does this include working or other things which do not consist of remembering Allaah but are useful, like eating and so on?

All perfect praise be to Allah, The Lord of the worlds. I testify that there is none worthy of worship except Allah and that Muhammad is His slave and Messenger. 

These actions were excluded from the dispraised Lahw (amusement) because they involve helping in goodness and in what is beneficial, but they are not the only excluded actions apart from all other permissible matters, because all permissible matters turn into acts of obedience with good intention, as Mu’aath, may Allah be pleased with him, said, “I hope for Allah's reward for my sleep in the same manner that I hope for His reward for what I do when I am awake.” [Al-Bukhaari]

As-San'aani said at the end of his interpretation of this hadeeth, “To conclude, permissible matters turn into acts of obedience with good intentions.”

If a person eats food to strengthen himself in order to perform acts of obedience to Allah and intends goodness by his eating food, then this is a praiseworthy act. This permissible action (eating) is considered an act of obedience for him; otherwise it would not be considered praiseworthy (if he did not intend good by it).

Allah knows best.