The report uses two metrics of economic mobility: absolute mobility, and relative mobility. Relative mobility is unitless because it's an elasticity: it measures how much parent income influences children income.
This is from note 13 in the report. Also, the authors didn't come up with this themselves. The data comes from here: http://www.iza.org/en/webcontent/publications/papers/viewAbs...
This explains nicely where the use of elasticity comes from.
Do you have other data that contradicts these conclusions?
That report again! All I see is: some professor came up with his own definition of economic mobility (some unitless score, what the hell is it?) and now we are supposed to take these conclusions as a gospel.
UPDATE: Apparently I can't reply to the comment below, so I have to do it here. The comment only confirms what I wrote and does not answer the question: what is that score? How is it computed?