When in doubt, if it's not a gendered, living thing, refer to it as "it".
For your specific example:
Russia was behind the Syrian regime since day one: arming it,...
That being said, if it said
Putin was behind Assad's Syrian regime since day one, sending "him"...
In this case, with the addition of Assad, it's ok to use "him".
We do use gendered pronouns with some things occasionally but it's not required.
For example, some refer to ships and cars as "she"... but you won't hurt any feelings by calling a ship or car an "it".