We analyze amplification of terahertz plasmons in a grating-gate semiconductor hetero-structure. The device consists of a resonant-tunneling-diode gated high-electron-mobility transistor (RTD-gated HEMT), i.e. a HEMT structure with a double-barrier gate stack enabling resonant tunneling from gate to channel. In these devices, the key element enabling substantial power gain is the coupling of terahertz waves into and out of plasmons in the RTD-gated HEMT channel, i.e. the gain medium, via the grating-gate itself, part of the active device, rather than by an external antenna structure as in previous works, enabling amplification with associated power gain >> 30 dB at room temperature.