Currently researched high-energy laser weaponry (the MIRACL laser, the Pulsed Energy Projectile and the Tactical High Energy Lasers) use deuterium fluoride lasers, which operate at the wavelength of 3800 nm. Visible light has wavelength range of 390 to 750 nm.
Even if the laser would use visible light, the beam would only be visible in medium that would partially reflect the light. As for example water particles (clouds, rain, fog) or smoke.
US Navy testing their THEL (note how the beam is not visible):
Also, from usefulness point of view, especially for man portable weapon, you don't want visible beam, as that would put shooter in tactical disadvantage. And indeed, the article you refer to talks about goals:
As a lethal system, a laser sniper rifle would be a formidable weapon:
perfect accuracy at any a range measured in miles, with no windage, no
drop, and no need to allow for target movement. And it would not give
the firer’s position away with a report, smoke or muzzle flash – all
the enemy would see would be the effect when it hits the target.