I'd say with all this, being a millennial (note: millennials are generally agreed upon to be in the 23-35 age group, with some deviation depending upon source), this is partly true, but also partly false.
I definitely want more money in my job, but if a raise isn't going to happen or no bonus, at least make me feel like the company appreciates me. That is, only if I deserve it. Shitty employees shouldn't get much in way of positive acknowledgement. At my company, that's generally the case as well - the so-so ones don't really get much in way of the atta-boys, but those, like me, who are good at their job, will get those.
But the whole concept does not revolve around simply money or praise, that is over-simplifying what the new workforce wants. This all comes back to the "work-life balance" and a positive workplace. We don't want to work shit jobs for money and that's all, we at least want to enjoy what we do and, barring that (can't always get what you want), at least try to make it a friendly work environment that makes working a little more enjoyable or at least less stressful. Obviously stress based upon pressing needs is one thing, but there is plenty of artificial stress introduced in some workplaces that does not produce a better employee.
The idea out of all of this is a happier employee = a more motivated and more productive employee. Over time, as the praise builds up, raises and bonuses should also come into play. I don't a damn gift card, but enough praise should wind up meaning you respect me enough to provide a raise because you fear losing me to a better paying job if you know what I have can transfer elsewhere for more pay.
So it's not so much we just want praise over money (or money over praise), in general, we are more vocal about demanding better work environments. It's that startup attitude vs corporate behemoths. And that's why some corporate behemoths are adopting more of a "startup" environment to cultivate happier employees. It works, you get a better product out of them. That much has been fully established. Make people feel like you care about them as an employee, that you respect their work, and that includes both praise and monetary benefits of some method be it a wage or bonus.