If you send an application to your boss, and the boss signs it, does that mean that you are ordering your boss around or that you are now your boss's equal? No, all it means is that your request found favor with the boss.
If your relationship with your boss is excellent, if you have been a sincere, loyal, and conscientious servant, then the likelihood of your request being granted is pretty good. The concept of "Dua" or prayer to God is similar... that you ask Allah for what you want, and Allah listens to and answers the prayer. For His loved ones, He grants the prayers more frequently than for others. This does not mean that the person who's praying is ordering Allah to do a certain task and has become His equal (nauzobillah). Please read the last sentence in the highlighted portion where Mirza Sahib (AS) says how humbled he was at the thought of Allah's kindness of granting him his wishes. And then he woke up.
If the act of praying to Allah and hoping for the prayer to be answered is to be equated with shirk or satanic activity, then no Muslim will ever pray.
Indeed I agree with this statement. This interpretation of the dream looks very logical to me.