"How is this chip stopping Microsoft from…"

I don't think it's supposed to impede competition with other portable music player makers. But it will thwart headphone makers. First, as you said, people won't be able to use their favorite pair of headphones with the new iPod shuffle. Now this is when things really get "interesting." Headphone makers won't be able to sell new ones if they don't play ball with Apple. The company probably has a licensing program, and accessory makers will have to pay a fee. Otherwise, the authentication chip will lock them out of the market. Lastly, as explained by the EFF, if they try to reverse engineer this stuff, Apple can invoke the DMCA to prevent them from interoperating with the new iPod shuffle.

This sort of stuff is already happening.

http://news.cnet.com/New-technologies-face-legal-headaches/2100-1028_3-997871.html

« Already, the DMCA has seeped into the market for printer cartridges and garage door openers. Printer maker Lexmark International and automatic garage door maker Skylink successfully have wielded the DMCA to ward off competitors who wanted to develop toners and garage door openers that would interoperate with their products. In both cases, the companies claimed that the competitors broke their protection measures. »