My takeaway is that I will not use their messaging system for private conversations if they get a license to "analyze, use and commercialize" what I am talking about.

Gmail is different:

"9.4 Other than the limited license set forth in Section 11, Google acknowledges and agrees that it obtains no right, title or interest from you (or your licensors) under these Terms in or to any Content that you submit, post, transmit or display on, or through, the Services, including any intellectual property rights which subsist in that Content (whether those rights happen to be registered or not, and wherever in the world those rights may exist). "

MySpace looks different too, note 'private' part which is mostly what irks me about LinkedIn's wording:

"you hereby grant to MySpace a limited license to use, modify, delete from, add to, publicly perform, publicly display, reproduce, and distribute such Content solely on, through or in connection with the MySpace Services [... ] except that Content marked 'private' will not be distributed by MySpace outside the MySpace Services and Linked Services. This limited license does not grant MySpace the right to sell or otherwise distribute your Content"