The big-picture view is given by Exhibit 1, and you can see it's really much more about analyzing all aspects of productivity (company-level, team-level, etc.) to identify bottlenecks around e.g. too much time spent testing over writing code, or senior developers stuck in endless cross-team alignment meetings which means management needs to identify a single person responsible for making final decisions quickly. So this is a document for engineering managers, not engineers.
But in terms of measuring actual individual developer productivity, if you read through all the verbiage it's really mostly just adding up the "planning poker" agile/sprint points that a developer delivers over the course of months. About which I have two main thoughts:
1) As long as planning poker is executed correctly -- i.e. always with unanimous consensus from engineers and without managers/PM's providing pressure -- this is actually probably going to be pretty decently objective, as a moving average. It's not terrible -- it's infinitely better than things like "lines of code". Although teams can also experience gradual "points drift" over the course of months, and points between teams can't be translated, so it can't be used company-wide or even year-to-year. But it will compare productivity between team members.
2) BUT, there's a huge risk involved because not all e.g. 5 point stories are the same, because of variance. Some are very straightforward where you know it's 5 points, while others are much more unknown, where the best guess is 5 points -- and it might wind up being 2 points but it also might wind up being 50 points. And so I could definitely see certain stories turning into "hot potatoes" nobody wants to touch because it's just too much of a risk -- it'll tank their average and they won't get promoted. And then everything just breaks down. Which means you either need post-sprint processes for "correcting" estimates and assigning a reasonable value for points done, or going deeper into "research" stories -- e.g. a 1-point pre-story to better nail down the actual size.