IIRC, Rotterdam has a 'gate' but it's right at the platform so you still should show up at 30 min there as well. It might just be screening, not ticket checks.

Eurostar only processes tickets for one train at a time and during a certain window so yes, you need to be at least be in line at 30 min.

Since the trains boards much faster then an airplane, they want you checked in, through Immigration, through screening and in the departure hall well before the actual boarding time of the train.

IIRC, Rotterdam has a 'gate' but it's right at the platform so you still should show up at 30 min there as well. It might just be screening, not ticket checks.

Eurostar only processes tickets for one train at a time and during a certain window so yes, you need to be at least be in line at 30 min.

Eurostar has such hard requirements due to the significantly more complicated check-in process. Since the trains boards much faster then an airplane, Eurostar needs you checked in, through Immigration, through screening and in the departure hall well before the actual boarding time of the train.

Rotterdam-Brussels is just a domestic train ride. No Immigration controls unless they're doing spot checks.