Most of the games you just listed were designed to be trilogies (or more) from the very beginning. For every sequel that was legitmately needed, there are 10 more that weren't. The concept of sequels in the video game industry revolves around money.
Why would it mention those things? The story for Max Payne 3 is set 12 years after the events of MP2, and in a different location.
This goes back to what I was saying earlier about them not rehashing the same setting, which would be an even bigger money grab.
Thinking on all the main features of Max Payne and it's story, that short description cuts every possible tie to MP1/2. It leaves the city that made up the games distinct atmosphere, it cuts Max Paynes job, it doesn't mention anything about Valkyre, Mona Sax, Paynes family or anything related to previous storylines. It pretty much makes up an excuse for throwing every possible element or angle of previous games out, just retaining the title to cash in on.
Why would it mention those things? The story for Max Payne 3 is set 12 years after the events of MP2, and in a different location.
This goes back to what I was saying earlier about them not rehashing the same setting, which would be an even bigger money grab.