noun
one machine; one device
Used when counting machines, devices, or mechanical equipment with the counter 機.
この工場には一機の大型プレスがある。
There is one large press machine in this factory.
noun
one aircraft; one plane
Used when counting aircraft, helicopters, or similar flying vehicles.
空港に一機の旅客機が着陸した。
One passenger plane landed at the airport.
noun
one life; one remaining life
Video game term for a single life or remaining life count.
残り一機でボスに挑む。
I challenge the boss with only one life left.
一台 is the general counter for machines and vehicles, while 一機 is specifically for aircraft or certain mechanical devices.
With negative verb, means 'not even one machine/aircraft'.
Compound of 一 (one) and the counter 機 (machine, aircraft). The reading いっき is a regular euphonic change from いち + き.