There are a lot of documentary films and books about this genre and era available these days, and I've seen and read some.
I think the compositional elements were largely the same as they were for British and American rock and pop music which was not synthesizer-based.
Some of the groups which made this music in the early 1980s described themselves as "non-musicians" who simply got ahold of the technology (sequencers and synthesizers, which in that era were rare and expensive) and learned to manipulate them. David Sylvian and the band Japan, including Richard Barbieri on synthesizers, have insisted on this "non-musician" description of themselves many times in interviews over the years.
That notwithstanding, what most groups were doing, as I understand, was to compose entire songs using the conventional guitar, bass guitar and perhaps real live drums played in the conventional way, but then to completely re-arrange and record the entire song using drum machine and programmed, sequenced synthesizer patterns which would take the place of the conventional rock instruments they had used to compose the song in the first place. Then they would overdub vocals, perhaps some real electric guitar in a few places (or real bass guitar in the case of the bands New Order and Orchestral Manoeuvers in the Dark, for example). I believe that Eurythmics (guitarist Dave Stewart and keyboardist/singer Annie Lennox) wrote all their songs in complete form on conventional guitar and piano first. I have read that Depeche Mode likewise composed most of their material on guitars and then re-built the songs entirely using programming and sequencers and elaborate synthesizer sound design, as well.
There are examples of 80s synth-pop songs and recordings whose use of technology seemed to steer or dictate the structure of the music. The best example that comes to my mind are the sampled percussion and band stabs, hits and loops that Yes utilized on "Owner of a Lonely Heart" and the album 90125, which were created by sampling performances by live musicians playing live instruments, which were then heavily digitally altered and manipulated using technology such as the Fairlight CMI. The session musicians and recording engineers employed by Yes and their producer Trevor Horn on that project went on to form their own band, the Art of Noise. The Art of Noise created compositions based on sequencing hits and loops created from digitally manipulated and altered recordings ("found sounds") and live musical performances -- moreso than playing synthesizers in the conventional way that a musician would play a piano or organ.
The producer Trevor Horn, who had a huge influence in this genre, was known to work by having existing conventional bands who played live instruments come into the studio with their songs already written. Horn would personally create a new arrangement and performance of the song using sequenced patterns on electronic devices including the Fairlight CMI and the Linn drum machine. Horn's programming work thus replaced most of the live playing by the actual band members who came to the studio. Thus he created an entirely new sound for bands including ABC and Frankie Goes to Hollywood.
Overall, I believe that the compositional and songwriting elements were the same conventional rock and pop elements, regardless of the startling new technology or how it was applied.