Completely baseless comment.

You can both learn calculus and play with toys.

And if calculus is presented as a fun group activity, like suggested in the article, I don't see why it would hinder the kids growth. It's the other way, really.

It looks like we have a misconception of the verb "to learn". Conveying some very general intuition of the subject from adult to a kid is not learning, actually. Learning assumes conscious effort to comprehend relatively complex things, constantly overcoming pain of uncertainty, most mathematicians will agree with me here. This is not what is usually expected from a kid. Don't do that.

There's also nothing stopping toys from being calculus-related either, although at the moment I can't think of any examples of such.

A toy calculator? :p

Imagine a toy truck that, as you drive it back and forth, plots the first and second derivatives of its position with respect to time on a little screen on the side.

Hmm, that's not the worst idea...

Nice idea for a toy! But learning an internal machinery of that process isn't that fun if you are not inclined for that kind of activity.