Why are Dutch people, language, and culture considered distinct from German people, language, and culture when German is such a wide category already?

Compared with some really different cultures like for example Canadian vs Malagasy or something, Dutch culture is not too dissimilar to German culture and they both speak West Germanic languages.

Yes, but this kind of a straw man argument. When comparing Canadian culture with Malagasy culture, then of course two European cultures like those of the Germans and the Dutch will be more similar. However, the same would go for Dutch and Polish culture or German and Greek culture when compared to the differences between Canada and Madagascar.

Germany and the Netherlands neighbor one another.

Europe is very diverse culturally and simply being neighbors does not have to say all that much. Germany borders a lot of different countries and its cultural closeness to either one of those countries depends on what is being compared.

For example:

In terms of the social scale of German society, it's closest to France.
In terms of its cuisine, it's most closely related to the Czech Republic and Austria.
In terms of traditional religion, it is closest to Denmark (for Protestants) and to Austrians/Poles (for Catholics).
In terms of language (excluding Austria and most of Switzerland) it is closest to the Netherlands.
In terms of values, Germany is closest to the Czechs.
In terms of architecture, Germany is typically Central European.

In comparison, for all the above the Netherlands are closest to Belgium in every regard … despite being adjacent to only two countries.

Germany and the Netherlands have existed in the same Empire in the past.

I'm assuming you're either referring to the Frankish Empire or the Holy Roman Empire. Again, this kind of a flawed argument because neither country existed during the times of these empires and many more countries have their modern borders situated within those former Empires. For example, Italy was part of both the Frankish Empire and Holy Roman Empire ... as was much of France.

"German" is already a broad category which encompasses many different subcategories, historical regions, cultures, and dialects (Bavarian, Prussian, Saxon, Swiss, Swabian, Styrian, etc.).

The modern Swiss or Austrians do not consider themselves to be Germans.

As for regional identities, those exist within the Dutch cultural sphere as well. For example there is quite a large north-south divide. Just because the Dutch language area is smaller, doesn't mean its cultural diversity is much lower than that of Germany.

The German region of Bavaria, though almost twice as large as the Netherlands, doesn't have the same amount of dialectal, historical, political cultural and religious diversity as the Netherlands do. Not by a very large margin.

So then, why aren't the Dutch and the Dutch language considered a type of German in the same way as the above groups? I guess that this could apply to Flanders, Luxembourg, and maybe Austria or Switzerland too.

Well, the Dutch language simply cannot be compared in this way to any German dialect. Its linguistic typology is far too different. To provide a rough comparison (and this only concerns the standard languages) the linguistic distance between Dutch and German is about equal to that of French and Italian, or Polish and Ukrainian.

Apart from linguistics, there is also a social dimension: the Dutch language has a literary tradition which goes back (at least) as far as German does. German has never been the official language in any current part of the Netherlands or Flanders; only Dutch and French have.

Perhaps this question is just borne of my ignorance because I'm certainly no historian, but I've been wondering about this for a while. Surely there must be some sort of point at which the Dutch were defined from the Germans?

And here lies the root of the problem with your question: it rests on the assumption that Germans (as a people, as an ethnicity) predate the Dutch; whereas the revers is true!

What we call Germans today (and retroactively - and often anachronistically) project back into history) are essentially a residual category. The Germans are (and I do not mean this disparagingly at all) are those West Germanic tribes/ groups which did not form a new and sharply defined ethnicity or nation during the Middle Ages or Early Modern Period.

The English did, the Dutch did and - in many respects - the Swiss did so as well; but the Germans did not. Only during the 18th century did the idea of a well defined German nation truly gather momentum.

After 1871, Germany found itself as one of Europe's largest and most powerful nations and actively promoted a kind of romantic nationalism to strengthen its newly found nationhood. Within that ideology, Germany and the Germans were no longer on the fringes of other European cultures; but formed it center. Suddenly, peoples like the Swiss, the Dutch, but also the English, were thought of as having sprung from German roots. After all, didn't the English come to England from Saxony?

As far as this pangermanism went, only the Austrians really played along with it. Which resulted, among other things, in the sometimes still vague ethnic/cultural relation between Germans and Austrians. The extent of Swiss "German-ness" never really extended beyond the use of standard German; whereas the English and Dutch pretty much ignored it completely or only used it in a kind of meta (Germanic rather than German) context.