The big issue AIUI is die-cut cardboard. The vast majority of modern board games come with several sheets of it to punch out small pieces (think coins or victory point chips).

Producing these (and other game components) requires specialized machinery which isn't made in the US. So even if someone did want to set up a board game manufacturing company in the US, they would now be hit by tariffs as they bought the machines they need.

Stegmaier says that possibly games where all the components are cards will be less affected, as there are companies in the US printing playing cards.

Die cut is one way to do it, but there are other approaches. I worked in a Christmas card factory for a bit and there are a lot of ways to make patterned bits of flat paper. The point about machinery import costs is spot on though.