The fact that you translate it in a natural English by "in this sport" doesn't mean that it's the correct way to interpret it. I think you already know it but I can't stress enough how important it is to differentiate "translation" and "interpretation".
Translation is basically re-writing something in another language keeping more or less the original meaning of the sentence. It doesn't have to be the equivalent, carry out the same degree of formality/politeness etc. It can be anything as long as it's coherent. Some translators completely change the meaning of some sentences just to keep a certain coherence and avoid confusion (example: jokes which are pretty hard to translate from one language to another).
Interpretation is what you think of when you see/hear something. It doesn't matter whether it's natural (or even coherent) or not.
Anyway, here while は can be translated as "in", I think to properly interpret it you should see it as being nothing more than a "subject (re-)introducer". It introduces the subject of the sentence (what is going to be talked about) and that's all. And since it's what is being talked about, it is obviously linked to a verb or adjective. But it's not linked as in "adverbially linked" but rather as in "semantically linked". It doesn't really impact how the action of the verb will be executed.
You can try removing it from the sentence:
海の上を走る水上オートバイから足に付けたボードにホースで水を送って、ボードから出る水の強い力で空中を飛びます。
It's not wrong but we don't really know what we're talking about here, even in your article where we know what the topic is, without a theme for the sentence it's a bit weird.
To sum it up, このスポーツは here is used to reintroduce an information that they brought up in a previous sentence, and make it the main subject of this new sentence. The previous sentence being in this case:
26日、香川県坂出市の海で、水の力で空中を飛ぶスポーツをしていた41歳の男性が亡くなりました。
Now as for このスポーツでは, it's fine. And to me in this case, で carries a nuance of limit, so では would mean something along the lines of "within". And while we're at it, I think that your translation "in this sport" would be more accurate for このスポーツでは than for このスポーツは. I would actually translate the は in your sentence by:
このスポーツは、海の上を走る水上オートバイから足に付けたボードにホースで水を送って、ボードから出る水の強い力で空中を飛びます。 : This sport consists of...
Which to me seems more accurate knowing the context.