OK, this might get a bit technical and is more suitable for the Kodi developers among us:
Streaming from .strm files just doesn't work anymore in Kodi,. After some investigation I discovered that the stream URL's redirect a couple of times and that the final URL, with a long one-time generated token, is the actual URL that streams. Only a custom python script (within a custom made Kodi add-on) that finds this final URL is the solution for streaming from Kodi if you don't want to use the PVR client (which is not so good for playback of the VOD section). It also might be the cause that some other Android and Smart TV apps don't work.
I assume that this measure has been taken to counter DDoS attacks that happened a while ago during popular football matches. This measure is fine with me, since it results in a stable service and I can work around it now.
Again, for most users this information will not help. But a to a Kodi add-on / app developer it might help to improve.