I'm sure they wouldn't, as it's not a US law. But a local company may be small enough not to have to bother, just as they don't have to provide certain US law based employer benefits.
> The second exception is for organizations with fewer than 250 employees. Small- and medium-sized enterprises (SMEs) are not totally exempt from the GDPR, but the regulation does free them from record-keeping obligations in most cases (see Article 30.5).