For the sake of this comment, let's define "templating" to be attempts to solve the problem "I need $FORMAT due to an existing constraint, but $FORMAT does not entirely meet my needs on its own" (in this article, $FORMAT is YAML). Additionally let's say that in order to be a "template" something must be a text file (e.g. exporting a database table as $FORMAT does not count as "templating" for the purposes of this comment).

I think there are three very different kinds of tools that people use for this:

1. Interpolation/preprocessor languages: This is what the author is talking about. There are delimiters/tags/sigils to distinguish "the templated parts" from "the rest" and the primary operation done by the template engine is substitution. "The rest" is literal content that's already in $FORMAT and it remains mostly/entirely unchanged during template rendering. Languages of this type are basically glorified `sed`. This can be nice because they're agnostic as to their embedding (any string will do) so they're very portable/flexible (you don't have to create "handlebars for YAML", "handlebars for HTML", "handlebars for CSV", etc; one implementation does it all). Languages of this kind can work in the small but don't scale well for all the reasons mentioned in the article/comments. The language doesn't know anything about the semantics of $FORMAT and that can cause all kinds of pain. Examples include golang templates, PHP, ERB, handlebars, the C preprocessor, Jinja, etc.

2. Compilers/code generators: These are "complete" languages that compile to $FORMAT. The difference between these and and interpolation/preprocessor languages is that the entire input is the language, not just specific chunks/tags. This kind of language can be nice because you have complete control and can therefore guarantee valid output and do tricks like supporting multiple different output formats for the same input, but the downside is that you're working with an entirely new language so there's a learning curve, you need specialized syntax highlighters and other tools to work with templates, etc. Examples include HAML, Jsonnet, Dhall, etc.

3. Embedded DSLs: Templates of this kind are valid $FORMAT from the beginning, but have embedded ways to specify transformations to be applied to the parsed AST. These languages are homoiconic with respect to $FORMAT. First $FORMAT is parsed, then the template engine iterates through the AST to perform evaluations, then the result can either be used as-is in memory or serialized back to (a possibly different) $FORMAT. This is sort of like an interpolation/preprocessor language with the evaluation order swapped: preprocessing is "run the template engine, then parse $FORMAT" while this is "parse $FORMAT, then run the template engine". A downside of this approach is that it is less general, e.g. it only really makes sense when $FORMAT has a well-defined structure (you probably can't template plain english sentences with this approach), but these days most "data languages" have converged towards being semantically equivalent to JSON (lists, dictionaries, and primitives) and this approach works well for any of them. An upside is that like compilers/code generators you can guarantee that the output will be valid $FORMAT no matter what the template looks like. Examples include JSON-e, Lisp macros, CloudFormation templates, etc.

It's unfortunate that all of these get called "templating languages" because they're very different beasts from one another, and usually when I see conversations about this stuff these distinctions get blurred and you end up with apples-vs-oranges comparisons. If I had my druthers we'd reserve the word "templating" for the first one and use different terminology for the others, but that ship has sailed.