A lot of things changed during that time, notably the job market. Getting a new job that paid $1/hour more would be more impactful than a $1200 stimulus check. People were getting raises much bigger than that.
The checks were not the primary driver of the economic changes
The article doesn't do anything other than quote the US Census Bureau.
Obviously you will have already read the citation in full, but for everyone else here is the full quote: "Stimulus payments, enacted as part of economic relief legislation related to the COVID-19 pandemic, moved 11.7 million individuals out of poverty. Unemployment insurance benefits, also expanded during 2020, prevented 5.5 million individuals from falling into poverty."
Again, this is from the US Census Bureau. It is being asserted in an official government capacity, from an governmental organization that has access to all the relevant data. If you think that they got something wrong you're going to have to offer something more compelling than some random theory you made up on the spot.
This one needs a little common sense. A one-time $1200 stimulus check is not going to lift 11.7 million individuals out of poverty in any meaningful sense, unless you're literally just looking at people within $1200 of an arbitrary cutoff and saying you "lifted them out of poverty" by bumping them over that threshold for the year.