Many do have exit checks (EU, most of Asia), but many don't (US, most of the Americas). I'd assume some of it in the US occurs when you buy the ticket... however, in some places you could still enter Mexico without a passport (returning is a challenge!).

The bigger issue is that Congress hasn't issued a specific mandate for this collection (by a private entity) and spending authority for the apparently ~$1B program. The article's concerns are for a more intrusive security state without congressional authority.

DHS’ current face scan-based program also may not comply with federal law. The program may exceed the authority granted to DHS by Congress because Congress has never explicitly authorized biometric collections from Americans at the border.26 Even if DHS has sufficient legal authority for the program, DHS has failed to complete a prerequisite public rulemaking process for the program, as mandated by federal law.