What’s the physics behind this lightning strike ?

There are many videos of this lightning strike on the internet. You can find them here : Romulus McNeill lightning - Google Search

It appears that a huge discharge rises from the ground to the man’s umbrella. Am I seeing this correctly ? What’s the physics behind this ?

First, you can’t really tell anything about the strike from the video, because the strike moves much faster than the frame rate of the camera. It’s a very incomplete look at what really happened.

I’ll link to an explanation of a lightning strike I made in a recent thread. So you are correct that the discharge you see rises from the ground, but it doesn’t terminate at the umbrella.

This video uses ridiculously fast frame rates so you can actually see how a strike propagates.

There’s an extensive explanation of what happened in the first article on that page of results you linked to. What you see near the man is probably an upward leader (or streamer), one which did not connect with the downward leader to form the main path of discharge - that happened nearby - otherwise he’d probably be dead.

The second (small) picture in this article shows this happening over water:

Another great picture of the phenomenon here:

I observed rising streamers in Rocky Mountain National Park in Colorado one summer. I climbed to the top of a col and looked down into a small bowl-shaped valley. A late afternoon storm gathered and I watched lightning flash up just in front of me. It was rose-tinged purple at the bottom.