In the quoted statement, they're reasoning from an accounting identity because they don't understand the underlying measure. There's a kernel of truth, but it's much more complicated than that.
Imports are subtracted from the GDP calculation, BUT, that's only because they're added in the equation as well as part of consumption/investment/government spending. So to capture only the domestic production, since it's hard to measure consumption/investment/government spending only on domestic inputs, you just measure them overall, add exports, and subtract imports.
So people see that in the equation imports are literally subtracted as a variable, and reason that if imports go up $X, that means GDP literally goes down by that amount. In reality — ignoring for a moment that we sometimes mismeasure consumption/investment/government spending, the net effect in the equation is 0.
ON THE OTHER HAND, in one way part of the GDP drop here is because of imports. It's not something you can cleanly calculate the way journalists often try to, because there's a lot we don't know, but picture this simplified example:
I'm a factory owner, and my factory uses a lot of inputs that we import from China. We normally spend $50k/quarter on investment (maintenance, new machines, etc.). But next quarter my short-term cost of Chinese inputs may double. It may make sense for me to front-load imports ahead of tariffs and defer as much investment as possible. I can't do that forever, so eventually the money will show up in the equation more-or-less where it would have otherwise.
And on top of that, there are a bunch of confounding factors. Over time, imports also make domestic production more efficient, so shifting to less-efficient US inputs (or simply paying the tariff) will slow the rate of overall growth. And some costs are passed on as higher prices, which reduces demand, and therefore reduces growth. And importing goods also means exporting dollars, which affects exchange rates, and therefore affects exports as well. It's all interconnected.
Calling it out when they reason from an accounting identity is really important, because it's a lot of what drives the misconceptions of Trump's protectionist advisors — they use the same reasoning in reverse to say that anything that reduces the trade deficit therefore increases GDP. But that's only true in an accounting sense! Reality takes more complex modeling, and has to account for all the interconnected pieces.