An EMP or "electro-magnetic pulse" has the power to knock out electrical grids and other connected systems. Imagine it like a power surge coming into your home that can destroy sensitive equipment such as radios, routers, laptops, etc. An EMP is like that but on a much larger scale. A nuclear weapon discharged in the atmosphere would generate a large EMP and it is feasible for such a pulse to destroy or render unusable the entire electrical grid causing widespread chaos and panic.
However, an EMP, unless it is either generated on a massive scale by a discharge from the Sun, is likely to be localized to an area or country so is unlikely to be the start of an extinction level event.
Note that the event, itself, may not be the ELE but it may precipitate such an event by, for instance, causing the markets to crash and bringing down governments.