The way he phrased it made it sound like EITC drawers aren't poor, and that's why it doesn't count. If the people earning it are poor, it should count towards figures that are helping the poor. It's also worth noting some programs phase out below the EITC phaseouts, so EITC helps keep these people from falling off a cliff on the income producing side or being punished too harshly for earning more money, while simultaneously providing additional benefits that financially incentivize employment.
I don't agree with Brueig here, but if his claims EITC, Medicaid, and CTC don't help alleviate poverty that's a damn strong argument he's making to eliminate them.