Chinese does indeed have templatic word order, but the categories in the post are not the real ones used. That source is laying out the typical ordering, not the required ordering.
Overall, I would say that word order feels about as flexible in Chinese as it is in English, but the specific rules are quite different.
The overwhelming majority of Mandarin Word order rules derive from a few principles.
- Phrases and clauses must following the order of the senses, and so
- follow the flow of time and space;
- You must proceed from general to specific, which entails that
- modifiers precede what is modified and
- Topics precede comments.
In harmonizing between the orders, Chinese word order is rigidly determined by pragmatics; however, since pragmatics can be flexible, the word order can also often be flexible. Sometimes additional function words can allow even more flexibility.
The only exception I can think of that violates these principles is that bare indirect objects must precede direct objects; however, you can often use "prepositions" to vary pragmatics.
The posted example gives two similar sentences. The first one is:
- Who 谁 on the road 在路上 in Chinese 用中文 (of) the/a stranger 向陌生人 asks/asked for directions? 问路?
At the highest level, the order can be represented as a topic-comment structure:
(Who) (.....asks/asked for directions?)
For these pragmatics, the order is rigid; however, the clauses could be reversed to make a similar, but different assertion:
(The asking for directions)问路 person/one 的) (is/was 是 who? 谁)
Both in English and Chinese, a few extra words are necessary.
Within the original comment (i.e., (on the road 在路上) (in Chinese 用中文) (of the/a stranger 向陌生人) (asks/asked for directions? 问路)), the last phrase serves as the sub-comment for the total comment, and the other phrases are like sub-topics. The subtopics have free ordering, but earlier topics scope over later topics in terms of generality, time, space, and modifications according to the five principles I listed above. Within each phrase, the order is semantically fixed.
The second sentence is:
- She 她 what time 什么时候 on the road 在路上 in Chinese 用中文 (of) the/a stranger 向陌生人 asks/asked for directions? 问路?
The first two phrases ((She 她) and (what time 什么时候) are just additional topics and can be put in any order with the other other topics; however, this will affect the pragmatics, sometimes severely. Some of the resulting orders would require very unusual communication needs, since earlier topics scope over subsequent ones pragmatically and semantically.
To get a sense of what the change of order of topics can do, consider the following English sentences that produce a similar range of possibilities with different specifics:
I played tennis in the park yesterday.
I played tennis yesterday in the park.
Yesterday, I played tennis in the park.
In the park yesterday, I played tennis.
Because of the requirement to follow the order of the senses, temporal topics in Chinese can never follow their comments or be made into comments by themselves. A time must exist before something can happen in it. On the other hand, durations must follow their verbs, since a duration cannot exist until the verb happens. Again, there are ways to work around these constraints if needed.
To obey the flow of time, places precede the activities that take place in them, but must follow when they represent the result of an activity. Two structures are necessary to distinguish the subsequent location of an agent and of an object.