The abductions came a day after the armed Syrian group seized control of the crossing along the Israeli border.
An al-Qaeda-linked group helped to seize the Golan Heights post, a gain of more symbolic than strategic value.
Damascus issued the warning despite the militant group’s capture of a major Syrian air base on Sunday.
The journalist had been held for almost two years by an al-Qaeda-affiliated group.
In the video, a group of about 60 men are shown in a hall listening intently to an Islamic State imam as he extols the virtues of Islam.
An advance on the city by government forces came under heavy fire from Islamist militants.
He praised cooperation between Kurds and the Iraqi army, and left room for more U.S. military action.
Officials said militants were driven from the dam in northern Iraq after being pummeled by U.S. airstrikes.
The counterattack is bolstered by U.S. airstrikes in a new phase of the American military mission.
The Islamic State is said to be giving them a choice: Convert and marry, or be imprisoned indefinitely.