UniGeezer posted a video of himself riding up stairs. The rise of each step was not so great as in your photo, there was more of a platform between each step, and Terry was doing it on a 36". But it was still amazing to watch.
I was riding with Jamie Mossengren. We were crossing a street, and when he got to the other side, he laid into the curb, causing a loud *bang". I am pretty sure there was no un-weighting happening. More likely the opposite, it seemed he pressed really hard into the curb. That curb was about the height of each stair in your picture. I’m pretty sure Jamie had to get his weight behind the unicycle as he hit the stair. I don’t know how that technique could be applied to more than one stair, however, as there is a great loss of momentum while crashing into the curb / stair.
There is a rock garden at the end of a long hill, on one of my local trails. At one point, I have to lay into a certain rock to get over it. Typically where I fall is the next rock after that first rock. Which speaks to the point I made in the last paragraph, that it’s hard to slam your way over successive objects. I ride with pretty high tire pressure.
The opposite technique would be to un-weight (rather than press/lay-into), but, again, is it possible to make successive un-weightings on each stair? I think not.
Theoretically, to make it up the stairs, you’d need maximum speed, maximum rotating mass, a high volume, low pressure, compliant tire, and an un-weighting that distributed itself over all six stairs.