No, a process in Critical Section can not be preempted. Best example to understand this is Priority Inversion:
https://en.m.wikipedia.org/wiki/Priority_inversion
That GATE 2013 problem is based on counting semaphore that can allow upto two processes at a same time in the Critical Section. There is no preemption there.
I haven't watched the video but I think you are not clear about the meaning of preemption and context switch.
Preemption: A process under execution(not in Critical Section) is preempted by a higher priority process, i.e., now the previous process is in blocked/waiting queue and the resources it had are now free to be used by the new higher priority process. Preemption is about getting hold of the processor to execute. Best example of preemption is any preemptive scheduling algorithm, like Round Robin.
https://en.m.wikipedia.org/wiki/Preemption_(computing)
Context Switch: Here context means information of a process, stored in Process Control Block of a process. Context Switch happens whenever a process under execution is paused to execute another process. This is done by storing info about the process so that when the process is loaded again, it is in the same state. Read "Steps" section in the below link:
https://en.m.wikipedia.org/wiki/Context_switch
I also suggest you to read about Spinlock if you don't know about it yet. It will deepen the understanding.