I think Putin's game is pretty straightforward. He's giving Trump a "bargaining chip" wink wink, nudge nudge, that he can "use" so Trump can give Putin what he wants and he doesn't have to "give up" anything of substance. The compounds they "took" are relatively unimportant, and most of the "staff" are Russians.
Quote
Altogether, the U.S. government employs more than an estimated 1,200 people in Russia. The majority are hired by the State Department, charged with running the U.S. Embassy and consulates, processing visas and handling other diplomatic tasks. But it also includes employees of dozens of governmental agencies and departments, like the Defense Department, the Agriculture Department, NASA and even the Library of Congress. Collectively, this vast enterprise is often referred to as U.S. Mission Russia or just Mission Russia.
....
The majority of U.S. Mission Russia employees are not Americans and won't be expelled: Of 1,200 people employed in 2013 in Mission Russia, 333 were U.S. citizens and 867 were designated “Foreign National Staff,” most of them probably Russian nationals. Using the 2013 numbers, if Mission Russia is forced to let go of 755 people, a majority of them would not be U.S. citizens and probably would not be expelled from the country.
(WaPo).

Putin is as easy to understand as Trump.

A well reasoned argument is like a diamond: impervious to corruption and crystal clear - and infinitely rarer.

Here, as elsewhere, people are outraged at what feels like a rigged game -- an economy that won't respond, a democracy that won't listen, and a financial sector that holds all the cards. - Robert Reich