Yes, for holders of the Deutschland-Semesterticket, the NRW mobility guarantee applies for journeys in NRW.
If the departure of the desired train deviates at least 20 minutes from the timetable, for example due to a delay or cancellation, you can either use a long-distance train (IC/EC/ICE), a cab, a taxi-like transport service provider, a sharing service (e.g. car, bike or e-scooter) or on-demand transport.
The additional costs will be reimbursed on request - in full for long-distance travel (IC/EC/ICE) and up to the applicable reimbursement limit for cabs, transport services, sharing services or on-demand transport; this is up to EUR 30 per person during the day and up to EUR 60 per person in the evening and at night from 8 p.m. to 4.59 a.m. nationwide.
If you use the mobility guarantee, you have to pay in advance for the use of an alternative means of transport. You can then simply submit a digital claim to have the costs reimbursed.
You have 14 days to submit the application. You can find everything else about the NRW mobility guarantee
here (currently only in German).
Other federal states have different regulations!