I think "are there any?" is essential, otherwise too much time is spent with the player attempting a capture with every one of his pawns.
I don't know how you've played kriegspiel, but in the club where I played it regularly we had three small tables joined together in a line with two longer one upended in the gaps. Then a board and set would be set-up on each table, the two players positioned at either end and the referee in the middle. The rules aren't completely trivial so not everyone was able to be a referee. The games tended to be quite long and we'd rarely get more than one finished in one evening (i.e. 7:30pm to 10:30pm).
I'm don't think any other chess variant would need a referee, unless there was a dispute, but in kriegspiel it's essential to have one. If an online version was done properly then a player's attempts to play a move, whether or not it was successful, would need to be conveyed to his/her opponent - sometimes the number of attempts and even the gaps between them can give you extra information.