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Additionally, with nonlinear loads, a multimeter must have DSP in order to measure properly.
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Proof to contrary here.
Those familiar with the arts of electronics circuitry thingies can see from the above explanation that the front-end known as the watt converter is ENTIRELY electronic and ANALOG.
Display is digital just like a common multimeter as there are A/D converters for the display output, but it's not just theoretical discussion.
What you'll see with many China made instruments is that accuracy specs are vague and only holds true under very narrow limits. For example, Kill-A-watt is only meant to be accurate with pure sine wave input waveform and it does not specify how it performs with spiky loads where peak to RMS ratio is very high.
Dismissing analog instruments as archaic and obsolete is narrow minded when many digital instruments have a lot of limitations such as power delivered through a dimmer, or at the OUTPUT end of PWM speed controller.