[Enthalpy]

If I see and interpret well, this was a fuel-air bomb:
  video.repubblica.it
A missile falls left of the street. At 0:05 some part of it jumps and falls on the street. A cloud forms and at 0:12 it ignites.

The newspaper tells "two missiles" but it's highly improbable that a first missile produces this cloud unintentionally and that a second missile strikes the cloud.

A fuel-air bomb carries only the fuel, not the oxidizer (nitro-, nitramines etc), and it mixes the fuel with ambient air before igniting it. This saves the oxidizer mass, so the same bomb mass produces 3-4× as much heat: observe the aerial wires moved much more by the second explosion. The explosion is also wider spread so it kills more troops. But it doesn't produce the huge detonation pressure of a solid explosive. It is inefficient against armor and little efficient against constructions. It's fundamentally an anti-personnel weapon.

It isn't immediately clear what military objective justifies an anti-personnel weapon here.

Good to know: if you see a cloud form after a first explosion, you have several seconds to duck. I thought it would go much faster.

[Enthalpy]

Videos of known fuel-air bombs show indeed the second explosion immediately after the first one. These more sophisticated weapons spread the fuel before reaching the ground. They use an explosive for that, it goes quickly.

Possibly the fuel-air bomb in the linked video is a recent approximate design meant to replace dwindling weapons stock. Or it uses a less dense or finer grained fuel that can't spread as quickly through air.

[RisingEastStar17]

It is known that usually such devices emit a fine mist of highly flammable gases such as oxygen and propane leaving a trail of these gases, which promptly ignite and explode when the main body of the bomb detonates. Perhaps one could modify and install a gas aerosol can to the main bomb?