Point 1: The Giant Squid is Architeuthis dux. The Humboldt (or the Red Devil or Jumbo) Squid is Dosidicus gigas
Point 2: The Humboldt Squid while large at ~2m in length and 45kg is not as large as the Giant Squid at 10-14m in length and 200-300kg.
Point 3: The Humboldt Squid can be found at depths of 0-1000m. The Giant Squid, while its true depth range is unknown, is likely deeper, i.e. you will probably not find it in scuba diving depths.
Point 4: The Humboldt Squid is found in high densities along the California coast. You can probably see them on a dive or catch them fishing. The Giant Squid remains elusive to scientist and the public. You can cannot see them diving and rarely (i.e. almost never) catch them fishing.
Point 5: The Humboldt Squid is not in the same genus or indeed the same family as the Giant Squid.
Point 6: To summarize the Humboldt Squid is not the Giant Squid.
Point 7: To say a Humboldt Squid is giant is fine, to call a Humboldt Squid a Giant Squid is wrong.
Point 8: If you are a member of the press (Not the New York Times! I expected better), please get your @#$% together. Its called research and it is is what you are supposed to do before you write your piece. You can see additional fun here. So no, thousands of Giant Squids did not wash ashore after an earthquake and Giant Squid are not invading the waters off Southern California.
Point 9: And don’t even get me started on all that is wrong with this video. I will leave that for commentors.