... how is circuit complete without a ground
The two black output terminals of the amp are almost certainly connected directly together within the amp, as well as to the amp’s circuit ground (to which the ground sleeves of the RCA connectors are undoubtedly also connected, by the way).
In bridged mono mode the red output terminals of the amp would both have full amplitude signals on them, with the polarity of the signal on channel B being the inverse of the polarity of the signal on channel A. The speaker won’t "know" that neither signal corresponds to the circuit ground of the amp. And the current supplied by each channel of the amp through the red terminal of that channel would be returned to the red terminal of the other channel, and from there through the output stage of that channel to the amp’s circuit ground.
From the perspective of each amplifier channel, a given output voltage will result in it having to supply twice as much current as it would have to supply under the same conditions in stereo mode, as a result the other channel of the amp supplying an equal and opposite voltage to the other terminal of the speaker. In effect the doubled current for a given output voltage results in each channel of the amp "seeing" the speaker’s impedance divided by two, which is why the amp is not intended to be used in bridged mono mode with speakers having less than an 8 ohm nominal impedance.
Regards,
-- Al
