OK, this is a key point, that you want only OPEN tabs to be tracked.
So, let me restate to see if I understand.
You would like a list of currently OPEN Chrome tabs, sorted by order of last accessed, correct?
If that is the case, I don't see any reason/benefit to use LaunchBar (and I'm a big LB user). Seems like a KM Macro, which can be triggered from anywhere, would do the job just fine.
Turns out there is already an existing macro that does something similar:
Find and activate specific tab (Chrome and:or Safari)
What it does NOT do is track and sort the tabs by last accessed.
But maybe you could try out that macro to see how you like it.
If you do, then maybe we could just modify it to do the sorting.