You could argue that "man-made machines", "biological machines" (all of life, animal, vegetal and fungus) and "simple matter machines" (like stars are engines or telluric planets are combustion heaters), even the "surface natural ecosystem of Earth", are all different
material implementations of machines: organized systems. Carbon-based, copper-based, hydrogen-based... you might map the whole periodic table of elements minus the rare column perhaps.
Ultimately you'd find a common unicity — like electrical charges, strong/weak force, arrangements of "gates" and "structure" etc. — but used in different ways (for instance iirc charged clouds of gas in space don't form new stars because gravity at close range is weaker than the charge that repels them, only strong enough at larger distances to hold them together; that's dramatically different from the use of charges in biological cells).
The cosmos itself is but a big machine. Who's to say we (I mean the whole planet, maybe star system, maybe galaxy itself) aren't actually just a single "cell" of the cosmos? That we are part of a much bigger machine, that we are like those processing units on dendrites in the article, if the universe is a big brain of sorts?[1]
These are all types of machines (X. process of information; Y. engines to convert energy; Z. structures that "restrict" "flow" like gates, transistors, cell membranes, dendrites; N...), which apparently may be expressed, materially implemented in different ways.
To take your question about logic.
If you mean the universal logic exposed above, I don't think so personally — merely because there's no evidence for it whatsoever, no observation; and there's also no need if we accept that from such "machinery" complexity may emerge complex systems (e.g. humans).
If you mean logic from within the human mind — and this begs the question of whether maths and physics are "invented" or "discovered" in the background — then we must assume a subjective answer, at best an aggregate of "non-disproved facts" that we can all agree on within normalcy (edge cases helping us understand said average norm).
"Logic" is but one of several operating modes. Are we more than that? Most certainly yes. That's the experience of all of us. Because perception is so centered on thought, we tend to overappreciate the importance of thinking in our lives, in our behaviors and even values; but the relative picture gradually revealed by biology and psychology and sociology and economics etc. is that we are mostly irrational, mostly automatic (trained habits, patterns recognition, educated intuition, etc), and actually very little in the way of "logical behaviors units".
I'll let you ponder the discrepancy from an absolutely (perhaps) low-level logical machine to the possibility of a chaotic non-logical emergent high-level behavior. What it means for life, for AI, and possibly much bigger or smaller things we consider "inert", for now.
[1]: I mean, look at the larger structures of the universe, tell me it doesn't look like a sample from a biological tissue... http://cosmology.com/GalacticWalls.html (figure 6: http://cosmology.com/images/darkmatterdistribution.jpg)
