We know that many ships in the Star Wars universe use repulsors for vertical flight.
Ordinary ships use them to hover:
A low, throbbing whine from above directed our eyes to the sky, where
we saw the black flying-toast ship descend on its repulsors and hover
perhaps four meters above the center of the lagoon, water rippling
Heir to the Jedi
As does Tarkin’s ship, the Carrion Spike.
Bright-side Coruscant air-traffic control directed the Carrion Spike
to the Imperial Palace, and there into a courtyard landing field that
was large enough to accommodate Victory- and Venator-class Star
Destroyers. As repulsors eased the ship down through the busy skyways
and into the court, Tarkin realized that the Emperor’s current
residence had once been the headquarters for the Jedi—though
practically all that remained of the Order’s elegant Temple complex
was its copse of five skyscraping spires, now the pinnacle of a
sprawling amalgam of blockish edifaces with sloping façades.
They also use them for vertical takeoff:
He ascended the boarding ramp and walked aft, settling into a seat in
the main cabin, the Theta-class shuttle’s only passenger. High
overhead, the Liberator’s hangar doors parted down the middle and
retracted, and the shuttle rose off its skids on repulsorlift power,
dropped its wings, and sped toward its rendezvous point, a pod-shaped
support carrier named the Goliath, which had recently arrived from
deepdock at Ord Mantell. Tarkin had a port-side glimpse of bleak Nam
Chorios as the shuttle angled away from the Star Destroyer, the
system’s sun providing barely enough light to illuminate the planet
let alone warm it to human standards.
As seen on speeders, repulsor containers, and so forth, repulsors don’t produce much, if any, wind. So ships that employ this technology wouldn’t produce a jet engine blast.
However, ships do have engines, which are used for non-vertical atmospheric flight and space flight. So if a ship is not taking off vertically, or just wants to build up some speed, it certainly can produce a blast.
For example, in Rogue One, Jyn was definitely knocked back by the engine.
Raindrops sprayed against her and a harsh gust of warm air dropped her
to her knees again. As the shuttle lifted off the platform, its engine
backwash built until Jyn was sliding back toward the platform’s edge.
She prostrated herself, clawed at the slick metal with her fingertips,
and only the shuttle’s final ascension saved her from the fate of the
stormtrooper she’d killed earlier.
Rogue One: A Star Wars Story
In the case of the video in the question, although the Falcon does not appear to be using its engines for its initial takeoff (probably employing repulsor lift), there appears to be some sort of ignition in the rear (accompanied by a roaring noise) once it’s gained a bit of altitude.
It is this, presumably, that blows down the gang in The Force Awakens, too, as mentioned here: