The short answer is that Privateer takes place around the same time as Wing Commander III. The year is actually the first word in the game. From the intro: "2669, Gemini Sector, Troy System..."
The long answer is the same, but with some interesting notes:
- When they started to make Privateer, Wing Commander III was two years away... so the choice of 2669 was to make sure it happened AFTER Wing Commander II more than anything else.
- Origin used 2670 instead of 2669 in some advertising. Case in point: https://cdn.wcnews.com/newestshots/full/IMG_0022.JPG
("The year is 2670...")
- Wing Commander III itself doesn't have a great understanding of when Wing Commander III takes place. While the manual makes it clear that Blair is being transferred to the Victory around July 2669, the actual game doesn't say this anywhere... and the intention may have been to set it as many as seven years later! Some background: https://www.wcnews.com/news/2015/02/18/startling-discovery-adds-new-wc3-facts-to-the-universe
(No later sources reference this and now totally contradict it... but it's interesting because that was apparently the choice made at a point when people *did* know when Privateer was set but nothing else that would later be established about 2669.)
- Righteous Fire is also problematic, as the intro begins "Jolson Pleasure Base. One year later..." implying that it's a year after a game established to have been set in 2669 (so... 2670.) The issue there is that the Kilrathi War is now established to have ended in 2669.