I’m not German, but isn’t it more about how they fit into society generally, and in the case of engineering places, how they fit into the wider manufacturing ecosystem?
the term has implications (you’d eventually expect family ownership, a “responsible” company with tradition and values, etc., although I think nobody would be surprised if they hadn’t any values apart from profit). Many of them fit into the manufacturing ecosystem as subcontractors / suppliers for bigger companies, and/or may be producing specialized goods or services.
Here’s a nice graphic from wikipedia about the relation with society, but it is a hundred years old now:
If you want to include small companies, the usual term is “KMU” (kleine und mittlere Unternehmen).
There is also the term “Mittelschicht”, which is about the middle of society, neither poor nor rich, and may not only be read as refering to economic wealth but also intellectual capital/education level (en: middle class, roughly).
That’s fine. The article/tag isn’t really about mapping “small engineering organizations” though. It specifically has to do with supposedly mapping “A place where a variety of parts are machined for different companies.” I think the fact that all you could come up with when you looked into the usage was “Regionally dependent, small engineering organizations” just proves my point that the tag is ambiguous and being used as a catch all on places that aren’t specifically machining parts.
In the meantime there’s already man_made=works for industrial manufacturing plants, which this tag is undermining. Like take Gearbox Group. They manufacture automotive parts. Why tag them as industrial=machine_shop in that case instead of man_made=works + product=automative_parts or whatever? Sure, as @SomeoneElse else says they are a “small engineering organization", but then it that doesn’t have anything to do with why product=* as an alternative to industrial=machine_shop makes no sense like he’s claiming. At least in the case of Gearbox Group man_made=works + product=automative_parts seems perfectly reasonable.
There’s plenty of other examples, Zagar Inc produces spindles. Why not use man_made=works + product=spindles there instead of industrial=manchine_shop?
Heck, take somewhere like King Machine Works & Powder Coating. They coat cars. It’s not even a place that machines parts.
There’s Hawboldt Industries. Currently tagged as industrial=machine_shop. They produce deck equipment. Again, not a parts machining place and there’s zero reason they can’t or shouldn’t be tagged as man_made=works + product=decks or whatever instead.
So aside from them being “small engineering organizations”, why exactly would tagging any of those places as man_made=works + product=* be nonsense? How exactly are places that manufacture decks or spindles machine shops?
Seconding the re-instating and thank you for telling of the English value “machine_shop” being there, currently use is 541 times industrial=machine_shop (soon there will be more), 10x craft=machine_shop (I like that one too) and 8 times machine_shop=* with 6 different values including meat grinder. 
“Machine shop” isn’t a craft. Machining might be, but machine shop? Nope. Have fun with the ridiculously needless and obtuse tag fragmentation though.
The majority of craft= are locations (=bakery) or jobs (=carpenter), not the craftsmanship (=metal_construction). Have fun with your view of the “ridiculously needless and obtuse tag fragmentation”. Other crafting can involving machining; does mean they are a “machine shop”.
Sure. That’s irrelevant to the issue of the tag fragmentation. I could really care less if the tag for machine shops is craft=machine_shop, industrial=machine_shop, man_made=machine_shop, or hell for that matter shop=machine_shop. What I have an issue with is that there’s like 7 different tags being used for machine shops. Have fun acting like the craft tag is something I care about though and not just the fact that there’s multiple tags being used for the same thing when there’s no reason for it 