We theoretically analyze the operation of a terahertz amplifier consisting of a resonant-tunneling-diode gated high-electron-mobility transistor (RTD-gated HEMT) in a grating-gate topology. In these devices, the key element enabling substantial power gain is the efficient 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 discussed in previous works, therefore potentially enabling terahertz amplification with associated power gains >40 dB.