One of my (many) bad jokes is that one of the German national past times is to create incredibly long string of compound words and then abbreviate them. Acronyms and abbreviations are very normal to find in both conversational and written German. German language materials whose intended audience is other Germans typically does have these linguistic shortcuts such as usw. (und so weiter/and so forth), Hrsg. (Herausgaber/editor), or GmbH (Gesellschaft mit beschränkter Haftung/ Limited Liability Company- although German LLC is slightly different than US LLCs). You'll notice that in these three samples there are similar Anglophone analogues (etc., Ed./Eds., LLC) which shows that German is far from unique in having acronyms and abbreviations, however they are more present in German in formal settings.

German military communications used both common acronyms and the type of special lingo common in any large special organizations. For example, the abbreviation "zdA" is commonly seen on surviving German military documents because it means "zu den Akten" (for the records) and sensitive transmitted reports would sometimes have "GeKdos" (Geheime Kommandosache/ top secret) which was an appellation omnipresent in wartime, as seen in the header of this intelligence report. The German language itself did not pose any hindrance to German military operations operations, but it was a handicap in the sense it was one of several ways the Allies were able to break Enigma and other enciphered German traffic. In the case of Enigma, the fact that the machine enciphered a letter as any letter but itself made these acronyms and abbreviations in military communications a weak link in the system. Thus the enciphered sequence for the three letters for OKW ( Oberkommando der Wehrmacht/ Military High Command) could be any letter but "O", "K", or "W", which made the system easier to break. Bletchley Park devoted a number of resources to parse out German military acronyms and other linguistic clues such as subject/verb placement to gain a foot in the door to deciphering enciphered traffic.

It should be noted that this was not so much a matter of the German language making Enigma weaker, but rather a flawed enciphering system that made the tendencies towards terse and abbreviated communication that are common in a lot of other militaries much more apparent.

I think a lot of that comes from using words put together rather than using several shorter words to say the same thing. Not so sure the total length of sentences will on average be longer?

The ww1 documents I have read in English (mostly war diaries, some copies of messages being sent during battles) have been full of abbreviations, and I doubt the German ones are any different, no matter if the words might be a few letters longer or not.