1) Yes Russians do use some American lingo, including military lingo - it's called loan-words.
2) Reread my post>every country with a standing army has veterans and people that sign up for service and later discharged>Army speak flows out into the population naturally, veterans or servicemen leave their posts and use this language irl.
My point being that this is universal for all countries with a military, has military lingo become part of common language, English, Russian, Chinese, etc. and it's not cringe, it's consistent with how language develops and grows over time. A specific usage becomes more widespread with exposure and time if it is relevant. Acronyms, slang and terminology spread naturally, regardless of origin.