They do collect Company/enterprise tax. It’s between 20 to 25%. They have a Tax Code, not simply a government decree.
The biggest Corporate (Company/Enterprise) tax collected is from oil and natural gas companies (45% or over) compared to say Construction or Telcos (around 14% and 17% respectively). These are state owned or the government has a large share in it.
In Australia, Transport/Railways, Postal Service, Energy/Electricity and Water are either partly or entirely owned by federal or state governments.
Employees in Russia do not pay Social Security and payroll tax. The employer (company) pays them.
http://www.worldwide-tax.com/russia/russia_tax.asp
Btw, China has the largest % of state-owned companies (96%), followed by United Arab Emirates (88%).
In the end it really doesn’t matter whether it is said to be an employee tax or an employer tax. It is the difference between what the employee gets in hand and how much it costs to pay it.
That said the tax wedge is not high compared to the other countries. It is higher than 13% though.
In 2014 someone getting €24k a year net in Russia means the employer spent 1.39 times more. At €24k/y level the tax wedge is slightly higher than in the US.
http://www.awarablogs.com/effects-of-putins-tax-reforms-on-state-tax-revenue-and-gdp/