"I heard Ka'b bin Malik telling the story of when he stayed behind from going out on the campaign of Tabuk with the Messenger of Allah (ﷺ). He said: 'The Messenger of Allah (ﷺ) came back in the morning, and when he came back from a journey he would go to the Masjid first and pray two Rak'ahs there, then he would sit to (meet with) the people. When he did that, those who had stayed behind came to him and started giving their excuses, swearing by Allah. There were eighty-odd men, and the Messenger of Allah (ﷺ) accepted what they declared and accepted their oaths of allegiance; he prayed for forgiveness for them and left whatever was in their hearts to Allah. Then when I came and greeted him, he smiled as one who is angry, then he said: 'Come here.' So I came and sat in front of him, and he said: 'What kept you behind? Did you not buy a mount?' I said: 'O Messenger of Allah, if I were to sit before anyone other than you of those who hold high positions in this world, I would find a way to avoid his anger. I am an eloquent man but, by Allah, I know that if I were to tell you a lie today to make you pleased with me, Allah would soon make you angry with me, but if I tell you the truth, it will make you angry with me, but I will still have the hope that Allah may forgive me. I have never been in a better position, physically or financially, than the time when I stayed behind and did not join you.' The Messenger of Allah (ﷺ) said: 'This man has spoken the truth. Go away until Allah decides concerning you.' So I got up and went away." This is an abridged version of narration.
It is this which the author cited the narration for. While the absence of the mention of a thing - in this case prayer - is not a proof that it does not exist.
Sunan an-Nasa'i Book 8, Hadith 44
Allah's Messenger (ﷺ) said, "While a man was going on a way, he saw a thorny branch and removed it from
the way and Allah became pleased by his action and forgave him for that." Then the Prophet (ﷺ) said,
"Five are martyrs: One who dies of plague, one who dies of an Abdominal disease, one who dies of
drowning, one who is buried alive (and) dies and one who is killed in Allah's cause." (The Prophet (ﷺ)
further said, "If the people knew the reward for pronouncing the Adhan and for standing in the first
row (in the congregational prayer) and found no other way to get it except by drawing lots they would
do so, and if they knew the reward of offering the Zuhr prayer early (in its stated time), they would
race for it and if they knew the reward for `Isha' and Fajr prayers in congregation, they would attend
them even if they were to crawl.
Sahih al-Bukhari Book 10, Hadith 49
"I saw Allah's Messenger (ﷺ) delaying the Maghrib prayer till he offered it along with the `Isha' prayer
whenever he was in a hurry during the journey." Salim narrated, "Ibn `Umar used to do the same
whenever he was in a hurry during the journey." And Salim added, "Ibn `Umar used to pray the
Maghrib and `Isha' prayers together in Al-Muzdalifa." Salim said, "Ibn `Umar delayed the Maghrib
prayer because at that time he heard the news of the death of his wife Safiya bint Abi `Ubaid. I said to
him, 'The prayer (is due).' He said, 'Go on.' Again I said, 'The prayer (is due).' He said, 'Go on,' till we
covered two or three miles. Then he got down, prayed and said, 'I saw the Prophet (ﷺ) praying in this way,
whenever he was in a hurry during the journey.' `Abdullah (bin `Umar) added, "Whenever the
Prophet was in a hurry, he used to delay the Maghrib prayer and then offer three rak`at (of the
Maghrib) and perform Taslim, and after waiting for a short while, Iqama used to be pronounced for
the `Isha' prayer when he would offer two rak`at and perform Taslim. He would never offer any
optional prayer till the middle of the night (when he used to pray the Tahajjud)."
Sahih al-Bukhari Book 18, Hadith 12
"Uwaimir, a man from Banu 'Ajlan, came and said: 'O 'Asim, what do you think if a man sees another man with his wife, should he kill him and be killed in retaliation, or what should he do? O 'Asim, ask the Messenger of Allah about that for me.'" So 'Asim asked the Messenger of Allah about that, and the Messenger of Allah disapproved of the question and criticized the asking of too many questions. Then 'Uwaimir came to him and said: "What happened, O 'Asim?" 'Asim said to 'Uwaimir: "What happened?! You have not brought me any good. The Messenger of Allah disapproved of the question I asked." 'Uwaimir said: "By Allah, I will go and ask the Messenger of Allah." So he went to the Messenger of Allah and asked him. The Messenger of Allah said: "Allah the Mighty and Sublime has revealed (something) concerning you and your wife, so bring her here." Sahl said: "I was among the people in the presence of the Messenger of Allah and he brought her and they engaged in the procedure of Li'an. He said: 'O Messenger of Allah, by Allah! If I keep her I would have been telling lies about her.' So he parted from her before the Messenger of Allah told him to separate from her, and that became the way of Li'an."
Sunan an-Nasa'i Book 27, Hadith 78