Veiled call to drink alcohol. That case when it's kinda lie (about tea) but everybody understand it. So it's a joke.

Also word "RYUMOCHKA" has miniature ending like "...OCHKA" which adds some effect of playfulness. Normal word construction is "RYUMKA" which is also suitable for this phrase - "Vypit' po ryumke chaya".

Russian spaces:

• particle "TO" of infinitve verb. Russian language doesn't use this kind of particles.
• english article "A" in front of the noun. Russian language doesn't use articles.
• preposition "OF". In russian, one noun dependence on another is indicated by russian cases. Here it's genitive. Shot (of what?) chaya. Nominative case is "CHAY".

English space:

• preposition "PO". Also genitive case indicator. To drink (what?) shot. Second indicator is russian word ending "ryumochkE". Nominative case is "ryumochkA". Also "PO" shows the need for a company, because if it's about drinking alone, the phrase will be sound like "Vypit' ryumochkU chaya".

Know better translation or have english corrections? Please, write comment or send me message about it!