That's just an formality. If there is a victim, ther eis an investigation.
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As the victim is royal, a very thorough investigation was done.
Each result of an investigation has to be given to the Public Attorney's office because it's not the police which decides if there was in fact a transgression against the law or not. Police workls for the PA office, so each arrest eg is cleared directly with the PA and there are laws how long somebody can be hold on PA authority till a judge has to be called in. Only if the PA decides to make the results of the investigation against a person into a case for court, proceedings actually start.
so at the moment there is no indication that Florian Moosbrugger has done anything wrong. Just standard procedure - and with so few articles, I guess nothing will come out of it.
As for Willem-Alexander in Lech and not staying at "Post" - AFAIK he and Maxima prefer the neighboring hotel when they are holidaying - as they did last February.