What could the amplifier be?
Neurons are amplifiers. Depending on the situation, a single transmitter molecule can trigger the release of a huge number of transmitter molecules to the next neuron. Glia might also have amplification functions. There are probably molecular processes in and around cells that qualify as amplifiers (one molecule of x triggers RNA production of z molecules of y). Microbes could act as amplifiers too: releasing hormone x could cause species y to multiply, releasing chemical z, which in turn increases hormone x.
Feedback loops aren't limited to single amplifiers. You can have any number of individual amplifiers in a loop. In the human body, chemokine A could cause vasoconstriction which causes the liver to produce less B, which causes the thyroid gland to produce more C, ... which causes gut microbe Z to release something which causes the intestinal immune cells to release more cytokine A. Amplifiers and feedback loops are everywhere.
Would you describe it as an energy boost?
No, especially if you are defining "energy" as "feeling more energetic" or "able to walk further". A power amplifier does "boost power" in that 1 mW of input power results in maybe 10 kW of output power, but the power source loses that 10 kW of power, so what is boosted is a matter of definition.
If you think of a basic electronic amplifier with a feedback loop, the gain is positive or negative. Typically it's negative, because the amplifier's gain without feedback might be 1,000,000 or more. Negative feedback is added to drop that to what is desired, such as making your earphone power levels 5x greater than the music device's "audio output". If the feedback goes positive, the output of the amplifier snaps to the maximum voltage (positive or negative) and stays there, locked in that state because positive feedback keeps reinforcing that voltage.
In terms of ME, there could be some feedback loop, involving just a few cells or maybe hundreds of "amplifiers" throughout the body, and some people are susceptible to having that loop go from slightly negative to slightly positive, and it only takes "slightly positive" to lock up. Evolution probably eliminated lots of variations that led to positive loops in the body. ME either isn't strong enough at reducing reproduction rates, or maybe there's a recent environmental factor that plays a role.