Wemos R1 D1 or NodeMCU + motor?
Fixed it! The reason is MOSFET requires 5V to be opened. Nodemcu and Wemos have pinouts which work with 3V only. I just replaced MOSFET with the similar one from the same manufacturer and with similar price but which works with 3V.

I also figured out that this problem fully independents from Arduino manufacturer by itself because even one of the cheapest Arduino clones - Dccduino works normally.