It might seem to answer a totally different question but I guess it can help you understand the situation in that Hadeeth also more easily:
... أَنَّ رَسُولَ اللَّهِ ص دَعَا أَبَا سَعِيدٍ الْخُدْرِيَّ وَ هُوَ
فِي الصَّلَاةِ فَلَمْ يُجِبْهُ فَوَبَّخَهُ وَ قَالَ أَ لَمْ تَسْمَعْ
قَوْلَ اللَّهِ يا أَيُّهَا الَّذِينَ آمَنُوا اسْتَجِيبُوا لِلَّهِ وَ
لِلرَّسُولِ إِذا دَعاكُمْ.
The holy prophet --peace be upon him and his household-- called Aba
Sa`eed Al-Khodry, he didn't respond back due to him being in Salah,
later that he went to the holy prophet the holy prophet criticized him
and said haven't you hear the words of Allah that "O ye who believe!
give your response to Allah and His Messenger, when He calleth you
[ref: فقه القرآن، ج1، ص: 121]
But some further explanation might be beneficial here:
If a father call his child and the child is at his/her Nafilah or any other Mustahab Salah, it is obligatory for the child to break the Salah and respond to his/her father. If the Salah itself is obligatory it will not be obligatory to break but as far as I can say it is recommended to end the Salah the sooner the better, with least possible Mustahab deeds and Dhikrs. Even some scholars have been reported to alter their intention of obligatory Salah to Mustahab Salah and then break it. Then you will notice that in a Hadeeth the holy prophet peace be upon him and his household has stated that "Me and Ali are the fathers of this Ummah" (أنا و علی ابوا هذه الأمة). Some scholars believe the Salah that the holy prophet has expected to be broken at his call for someone has been Nafilah but most believe this is true also about obligatory Salah.
Responding back a call is a specific case of attending and being at someone's order, according to that verse even the smallest request of the holy prophet should be preferred over Salah. However, according to the other answer given by @BattleOfKarbala (now deleted) the missed Salah by Imam Ali peace be upon him was perhaps already performed while being sat.
According to Shia Ahadeeth pure belief to Allah (یعبدوا الله مخلصین له الدین) is the spirit of Rasulullah peace be upon him and his household, performing Salah (یقیمون الصلاة) is the spirit of the guardian of the believers peace be upon him, and paying Zakah (یؤتون الزکاة) is the spirit of the Ahlul Bayt peace be upon them, if I have not misused the phrases. In that scale of understanding the events like the one you have mentioned in that Hadeeth will find new aspects that will require more prerequisites for fully being understood and hopefully this much suffices here.