AFAIK there's no standard for monitoring of AC adapters and I'm not even aware of any adapter capable of this.
This is the first time I hear about such feature and I assume DELL is using some proprietary method for this, which is not disclosed to others.
I have did a bit of RE and now I know how Dell's app works. It captures BIOS events and process it and I can do that myself. The one thing I was a bit disappointed to find out is that it does not read AC adapter parameters directly, it only responds to events. But I would guess that that data could still be read if someone would know where exactly to read it from.
By the way, not only Dell, but also HP and Lenovo offers the same feature to detect incompatible PSUs.