My work machine is 10.12 and patched today.

Sierra and El Capitan is covered too.

https://support.apple.com/en-us/HT208331 - see Kernel entries.

10.12 is Sierra. I cannot see any security update in the updates tab of the App Store app, nor in the list of updates that were installed in the last 30 days.

This update shipped to 10.12 on Dec 6 as 10.12.7.

No, there is no macOS 10.12.7 release

https://support.apple.com/downloads/macos

Perhaps you're referring to a release on Dec 6 labeled as "Security Update 2017-002 10.12.6," which does not appear to include the Meltdown patch for Sierra.

I might be super confused about versions, but security update 2017-002 Sierra claims to include the patch according to this page: https://support.apple.com/en-us/HT208331

I'm on 10.12.6 on a Mid 2011 MacBook Air 13": "No Updates Available"

Edit: I see, there is a confusing typo in om2's comment (it should be 10.12.6 not 10.12.7). I am wondering why this update does not show up in my list of installed updates. What a mess.

It was released as Security Update 2017-002 and 2017-005 for Sierra 10.12.6 and El Capitan 10.11.6 respectively, not as point version updates.

No, 10.12.7 is the right version. It's "available for" 10.12.6, which means that is the version that will be offered the update. I am not sure why it's not showing up for you. Consider contacting Apple support.

Only fixes Meltdown but not Spectre.

They said that they've only patched Meltdown so far.