Random guesses:
*All the train numbers are even. Departures from Moscow even-numbered, arrivals to Moscow odd-numbered?
*There are two trains 30 and two trains 56, each departing at the same time with the same first word (destination?) but a different second word. I'm guessing sections, like the Lake Shore Limited or Empire Builder?
Not a guess but an observation: unless there's a whole other set of columns right of the ones shown, only one train departed in the morning, #16. (I'm not counting #44, everyone considers a 12:35 am departure as "really" the last departure of the previous day.)
You came very close with your first observation. This is the Moscow station that is the head of the line for the Trans-Siberian Railway, so all trains departing here are eastbound. Just as in the U.S. and Canada,
eastbound trains are even-numbered.
In World War I a U.S. mission was sent to Russia to try to help them better operate the line from Vladivostok, where U.S. supplies for the Tsar's army were piling up. American rail operating men worked as far west as Omsk. It was a thankless job because - of course - some of the Russians hated taking advice, some of the Americans were undiplomatic, and then the October Revolution came, followed by chaos. You may know that there was an entire Czech army division fighting its way home from their Austro-Hungarian role on the Eastern Front by way of the Trans-Siberian Railway. So the Americans were always being accused of favoring one faction or the other, while they saw themselves as an essential part of getting post-war food relief to European Russia.
They pulled out division point by division point as the Bolsheviks got things under control. They left behind some North American ideas, apparently including train numbering conventions, big steam engines with pulling power and chime whistles, and centralized dispatching with train orders.
The column on the right of the board shows days of operation. Some of those trains run on alternating days to different destinations. Don't tell Amtrak, but some of these sleeping car trains run on stranger schedules than tri-weekly. The Deutsche Bahn has a good way of showing it visually. The attached calendar shows one Siberian train's departure dates in green. Quite a few depart on odd-days only or even-days only and are meshed with another train running another branch on the opposite days. So an American copy might be a Crescent that would go from DC to New Orleans on odd days and to Mobile on even days. (Shhhh!).
This is a lot easier booked in advance. On this 2010 trip I was in line to obtain a ticket in exchange for my home-printed voucher and the businessman in front of me got in a row about travel dates with the overheated agent (no AC in July, with the air hazy from forest fires). I could see that some of the queue and bystanders were anticipating the foreigner having trouble next, but it went smooth as could be. Had changes been necessary, though...