It is true that LX64 took-off at 14:16, but the doors were closed at 13:44 and while LX1249 landed on 12:56, it was at the gate only at 13:01. If you add 10 min to get off LX1249, this is only 10 min before the scheduled departure time of LX64. It is certainly possible to make it to from gate A/Bxx (arrival of LX1249) to gate Exx (departure of LX64) until 13:44 if you can navigate through ZRH airport well and quickly, this is certainly a challenge given that you have to walk to passport control, take the Heidi-train, find departure gate, pass document control for US flights ...
So, I think that LX may have automatically re-booked the OPs family members.
Concerning the "delay" of LX1249: This is very normal for LX operations - LX1248 arrived on time in ARN (even 4 min early), but a turnaround time of 45 min is simply impossible to handle for a fully booked A320. Plus the flight time was a couple of minutes longer than ususal (2h22)