I am not a lawyer, nor do I play one on television. However, I am a mathematician, a field in which the precise use of language is known to be difficult and sometimes unnatural or counter-intuitive.
Having said that, here is my reading.
Specifically, the law offers the wording:
... 'order with obligation to pay' ...
That seems to indicate that "order" or "place order" by itself is not enough, and that one must explicitly state that placing the order incurs an obligation to pay.
So "Place order" is not ambiguous in the sense that it is clear that you are placing an order. The law seems to be stating (implicitly) that placing an order does not explicitly carry the obligation to pay, and hence the requirement for the extra words to make that clear.
When using plain language is it difficult to construct a sentence that a determined adversary cannot misconstrue. Following the suggested phrasing closes off some options for such games.
In German, it is “kostenpflichtig bestellen“, which is also quite clear and I have to admit I like it. The button cannot be misunderstood and it seems silly to claim that it is in any way an inconvenience to a honest trader that they have to put “kostenpflichtig bestellen“ rather than just “bestellen” on their websites.
In contract terms, yes it is ambiguous - especially now legislation offers an alternative phrase.
As a consumer, perhaps I think place order means let me try it for 30 days and decide if I want it or if I want to return it. Or some other variation which means I don't expect to have to pay you anything.
Whether I am being deliberately obtuse or not, few traders will want to get into legal nonsense over online orders which are not necessarily very profitable (hence any profit is lost as soon as there is any dispute costs).
If the law offers an acceptable phrase, it is reckless not to adhere to it as otherwise you end up in a court discussing sematics of english phrases rather than whether you are owed money or not.
You're saying "Place order" is ambiguous?