It's important to note that between the venting and the takeoff there's a cut in the video.
The venting is maybe a test for—or an auto-regulation of—the air intake venting system.
The engine air inlets of the Hornet, like that of the F-16, are of a simpler "fixed" design, while those of the F-4, F-14, and F-15 have variable geometry or variable intake ramp air inlets. This is a speed limiting factor in the Hornet design. Instead, the Hornet uses bleed air vents on the inboard surface of the engine air intake ducts to slow and reduce the amount of air reaching the engine. While not as effective as variable geometry, the bleed air technique functions well enough to achieve near Mach number 2 speeds, which is within the designed mission requirements.
The conditions being wet/humid would explain the water-vapor like venting.
From the F/A-18C manual:
Part of the boundary layer air is bled through a fixed area outlet into the fuselage boundary layer diverter channel. The other part exits on top of the wing through inlet duct doors, when open.
Here are some photos that show the vents.
(Source) This highlights the intake / vent positioning.
(Source) This is a Swiss F/A-18C with a better view of the vents. Judging by where the leading-edge root extensions meet the wings, it's a solid match for the position at least.
What about the two round vents on the left side?
From this cutaway in Spanish (item 54): They are "air purge grilles / refrigeration". Given that the air conditioning pack (ACM) is also near this area, they're maybe the outlets of the pack. Like the grills on the bellies of airliners.
I found it twice more, in each time the venting is on the left side as the engine speeds up. It's very plausible to be ACM related. Either venting of the intake air to reduce the amount of bleed air going to the ACM, or it's the ACM handling the excess bleed air.
Is it something to do with cockpit pressurization?
The pressurization schedule shows that the cabin pressure is not reduced when on ground, so it's not venting of the cabin air.
Is it fuel vent test?
According to the manual, no.
All internal fuel tanks are vented through the vent outlet in each vertical fin. The external tanks are vented through the vent outlets in their individual tanks.
The intake/exhaust of the APU on the F/A-18C is on the underside.
Focus on the puddle I marked above, even play the video frame-by-frame using < and >. You'll see that the venting happens when the thrust is increased.
Whether it's air intake and/or ACM related, it happens when the engine initially spools up.