Well, those four (Program, PROJECT, BC, and Mecha) ARE linked. However, I never thought of Arcade being a part of it. I assumed that it'd be separate, due to their retro particles being reminiscent of much older games-- games which would not usually exist at this point in time in the PROJECT Universe.
If we were to line up our world with the PROJECT world, the Mecha vs Battlecast (War of Metal) would take place in 2020 or so, the rise of the PROJECTS (First wave of PROJECT skins-- Overdrive) takes place in 2030-2040, as evidenced by the advanced technology in the city in Overdrive (Neo-Ionia, I believe), the G/NETIC program (Disruption and probably Hunters) would take place around 2050 (hehe Blade Runner 2049), as Ashe, Ekko, Kat, and possibly Vi and Vayne are much more advanced than the previous PROJECT models, and the Program skins would most likely be late 2070 or early 2080 (hehe Cyberpunk 2077).
Very few games in our late 2010s are pixelated, which leads me to believe that the same could be assumed for PROJECT. Now, I'm not against the idea, but I personally don't think it'd take place at the same time. Perhaps BEFORE the War of Metal, but I doubt they're connected to the PROJECT Era.