Hi there. The portrayal of the Persian buildings in your linked screenshot are definitely more reminiscent of later Muslim buildings, such as the Blue Mosque in Istanbul, but the blue-colored bricks probably harken back to ancient Babylonian buildings as well. Most famously, the Ishtar Gate, a Neo-Babylonian ceremonial gate from the city of Babylon, was built with blue glazed bricks. Now, the entire city of Babylon wasn't built out of blue bricks, but some of the more ceremonial buildings were, and the city was probably more colorful than some other depictions of Mesopotamian cities may lead you to believe.

As for "Persian" buildings, we know quite a bit about how the palaces and tombs of the Achaemenid kings look based on their archaeological remains. One of the main capitals, Persepolis, has been beautifully reconstructed digitally here, and the royal tombs at Naqsh-i Rustam are incredibly astounding as well (although it is unknown if the reliefs on these tombs would have been adorned with any color).

Only one building remains from the Parthian (i.e. Arsacid) capital of Ctesiphon, and that building only gives a glimpse at the immensity of their architectural style. Nonetheless, we can say with certainty that the city was not ablaze with blue and gold surfaces.

This is only a preview of what we know about ancient Persian buildings. If you wish to see more, I recommend checking out Michael Roaf's Cultural Atlas of Mesopotamia and the Ancient Near East, which contains many beautiful pictures of archaeological remains from many of these sites, as well as maps and reconstructions. For something that focuses primarily on the Arsacid and Sassanian periods, Rahim Shayegin's Arsacids and Sasanians is great and recent, but a bit short on images.