This seems very unlikely compared to the obvious answer that they added a crappy antenna to keep their BoM and assembly costs low.

The radios on these are weak and adding an Omni antenna is exceptionally unlikely to violate EIRP.

Could this design accidentally radiate something it's picking up from the board outside of 2.4ghz? Sure.

But practically it's quite unlikely to in this context.

2.4GHz is already incredibly crowded and prone to interference (in urban environments). I remember once picking up emissions on a Bluetooth headset from a leaky microwave oven.

As an individual this is mostly true unless you're touching broadcasting proper. As a business this is absolutely not true and noncompliance is a ticking time bomb that will bankrupt you.

As someone in Southern California who uses HAM, this is both true and not true. There's an older gentleman who has already spent time in jail for sitting on frequencies without a license repeatedly. After he got out, he jumped right back on it. He's got tens of thousands if not more in unpaid fines, but as far as I'm aware they cant get blood from a stone.

Another anecdote, dozen or more years ago a friend had a fault cable modem that was spitting out radio traffic I assume on some important frequencies in a dense area. They got a knock on the door from an FCC team who were tracking the interference down.

The author is German and lists German contact information. They're a lot stricter in the EU about this.