There are actually 2 factors here (both of which are in the OP's favour):
- On the 'Zugbindung' tickets, you have to travel on the specified long-distance trains (eg: ICE, IC/EC, D, CNL, EN, etc). However, if local trains (RE, IRE, RB, S), form part of the ticket, you don't need to travel on the specified local train, and can travel (once) on any other local train on that route the same day (or even first the following day, on some tickets). The ticket should say something like "NV = NAHVERKEHRSZÜGE VOR / NACH FERNVERKEHRSZÜGEN; GILT JE FAHRT MAX. 1 TAG BIS FOLGETAG 10 UHR"* (Some tickets don't explicitly have this condition written on them, but I think if it says "NV" for part of the routing, that rule still applies. The tickets do say that the routing written under the 'Fahrkarte' heading is binding, while the routing written under 'Ihre Reiseverbindung' is only advisory).
- If you miss a connection because a previous train on that ticket was late, then DB will allow you to take the next train. (In the case of short, local train, like this example, you can just jump on. However, for long-distance trains, I think you're supposed to check with DB first (eg: with the conductor on the delayed train), and if you're booked on a cheaper train (say IC/EC) and missed the connection, I'm not sure they'd would automatically let you take an ICE instead).
* NV = LOCAL TRANSPORTATION LINES BEFORE / AFTER LONG-DISTANCE TRAINS, IS PER TRIP MAX. 1 DAY UNTIL the following day 10 CLOCK