There's only 2 "abort" exceptions:
a) Double fault exception. This happens when trying to start one exception caused a second exception; where the instruction pointer (saved by CPU when starting the double fault exception handler) could be from the original instruction, the first exception, the second, something else or nothing. In this case, because the CPU couldn't start the first or second exception handler you can't return from the double fault to the second (or first) exception handler anyway.
b) Machine check exception. This is purely for hardware faults where you probably don't want to assume that memory, or caches, or the CPU actually work. You can't expect "guaranteed behavior" from faulty hardware.
Note 1: Technically, for some causes of machine check, you can return to the precise location of whatever happened to be interrupted by the exception; you just need to be very careful about determining if you can/can't return (and need some way to fix/work-around the hardware problem/s so that returning from the machine check exception handler won't just trigger a second machine check exception).
Note 2: It's perfectly possible for the exceptions preceding a double fault, or machine check, to be caused by something that isn't an instruction at all (e.g. caused by an IRQ). In these cases "the precise location of the instruction causing the exception" would be "the precise location of something that doesn't exist". Intel's words should be interpreted as being conditional (like "an exception that permits neither precise location of the instruction causing the exception if there is one, nor restart of the program that caused the exception if there is one").