An amp that I would consider to be a true 'digital amp' would be one where the process of conversion from digital to analog happened only at the output, IOW that the entire circuit is one big DAC.
@atmasphere - interesting. I could be wrong, but my reading of the Lyngdorf integrated (and other "digital" integrated amps that are now coming out such as the new NAD DirectDigital) would seem to match this architecture. As best I can tell, there is no "analog audio stage". It seems like they are using the actual digital pulse output of the DAC chip to drive the amplifier output transistors. In this sense, the amplifier power output stage is essentially acting as the "DAC I/V" stage (basically bypassing all the analog and preamp stages in between). It's really not a "digital amplifier" because it is still an analog translation (which is required in any sense of audio anyways). I could be completely wrong here, but this is what I am assuming based on how they are describing the product.
I'm not sure how well this actually works. Some people just love the Lyngdorf, but I would actually want some sort of Class A discrete analog stages in between to help shape the sound and reduce the square wave effect of the DAC pulses - in addition to providing a very strong signal to drive the impedance of the amplifier. I think the Lyngdorf could be very crisp/clear sounding for some people, but I think it could go too thin and solid state sounding.