I don't claim to know anything about how Chrome works, so could be completely wrong in this, but my sense is that it is part of a broader desire to tie together tracking across all devices. Cracking that nut is very difficult from an analytics perspective, and having people logged in to Chrome across all devices provides a very convenient GUID for matching against AdSense units, DFA tags, GA tags, etc.
So the value in this play is not necessarily in knowing everything you do online, but simply knowing that you are who you are regardless of device or Chrome instance. That means data about you is consistent, and can feed into the broader targeting algorithms to serve you the right ad, at the right place, at the right time.
Again, I don't know what data Chrome makes available to Google's ad services, so please tell me if I am in fact incorrect here.