Thank you for the valuable information, @Johannes! According to the link it is only required that one of the travellers loads the ticket into their Reisplanner app:
One member of the group books the ticket, which is bought and paid for online. The details of each one of the passengers are entered.
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When your order is complete, you can choose to either download and print your e-ticket or to load it in the Reisplanner Xtra app
Am I interpreting this correctly? That would only require one of the group to gather the whole names and birth dates and order the ticket.