Uh yeah you need a spring compressor, you need to do it the way he did it, and make sure you do it correctly. I've seen springs shoot off and go through the fender. Not a good place to try new techniques on.

Take the whole damper out but make sure you leave that top bolt on, then use a spring compressor to keep the spring compressed. Don't try to save 10 mins. Then undo the top bolt and change the strut.