If I have a non-RTOS single core system, can one task, say taskA interrupt another task, say taskB, where neither taskA or taskB are interrupt routines? Or is interruption of one task by another only possible through ISR(interrupt service routines) on non-RTOS systems?
For your system to have more than one non-ISR thread implies that there is some sort of multi-tasking - and multi-tasking is not exclusive to an RTOS. One task "interrupting" another is known as preemption. Preemption requires a preemptive scheduler, while an RTOS is necessarily a pre-emptive scheduler, so also are Windows and Linux for example - but these are not real-time since scheduling and preemption is not deterministic.
Preemptive multi-tasking is necessary to support preemption, but real-time deterministic scheduling is not required. Preemption however is not necessary to multi-tasking; some systems (Notably 16 bit versions of Windows prior to Win95, and MacOS prior to OSX) are cooperative multitasking systems where a running task must yield the CPU to allow other tasks to run.
In a preemptive multitasking system, the scheduler executes on exit from the interrupt context and whenever a task invokes a schedulable event (such as giving a semaphore, queuing a message or releasing a mutex. If when the scheduler runs a task becomes ready to run and the scheduling policy requires or allows it to preempt the current task, a context switch will occur.
So in short one non-ISR thread or process "interrupting" another requires an OS that supports preemption, which need not be an RTOS.