I see your objection that to consider agriculture's decline indicative of the future of labor in general could be considered cherry-picking, but I think the video at least attempts to respond to this charge, explaining why its author does not feel other industries will "pick up the slack" in the same way in the future as happened in the past for jobs lost to automation.
[For what it's worth, while enamored of the dream of leisure-society utopia, I am quite skeptical of the author's assessment of the current state of progress on various forms of automation (and thus, a fortiori, of the projected speed at which such automation will take off as ubiquitous in the near future). But I did want to defend them against the charge of not even considering the idea that jobs will simply shift to other industries.]
For example, within the first few minutes they show this graph: http://i.imgur.com/IDXYI9Y.png
But the U.S. Bureau of Labor Statistics shows this: http://i.imgur.com/BPNyjM8.png
They've excluded other industries in forming their basis and it's clearly cherry picking to fit a narrative. I like the idea of a fully-automated utopia as much as the next person, but jobs are simply not going to disappear - they're going to shift industries.