The Mekhilta reads the phrase "By the greatness of Your arm they were struck still as stone" as describing a specific historical moment. When the Israelites emerged from the Red Sea, the Amalekites did not wait. They immediately gathered all the peoples of the world and assembled a coalition army to attack Israel while they were still wet from the crossing.
The timing was calculated. The Israelites had just endured the most intense experience of their lives — walking between walls of water, watching the Egyptian army drown behind them. They were exhausted, disoriented, and vulnerable. The Amalekites saw their moment and seized it, rallying every available nation to join the assault.
But Moses prayed. That single act — one man lifting his voice to God — was enough to neutralize the combined military force of every nation the Amalekites had gathered. The coalition armies were struck still as stone. Not killed, not scattered, not defeated in battle. They simply froze. The Hebrew word suggests a petrification so total that living warriors became indistinguishable from the rocks of the desert around them.
The midrash (rabbinic interpretive commentary) highlights the absurd asymmetry between the threat and the response. An entire world coalition versus one man's prayer. The prayer won. This passage establishes a principle the rabbis would return to again and again: the power of a righteous person's prayer exceeds the combined might of all earthly armies.