And there is more logic to not allowing trades during playoffs than to allowing them.
1. A GM of a team in the finals might not be planning or even know their off-season plans before they know if they won or not. They are unlikely to be as involved in negotiations as eliminated teams' GMs and as this isn't the NHL life, you can't expect people to be constantly "working the phones" even if they are still in the playoffs
2. As a result, some trades may well be sealed because of less competition. I doubt this was the case in such an inconsequential trade but it is possible that if Toronto or Riga wanted a piece from Helsinki, New York would have found it more difficult to acquire it. By allowing mid-playoff trades, New York gets that advantage by virtue of being less good than Toronto and Riga.
3. The Hamilton and Kyanon rights trade was particularly bad as if it was processed, you're basically saying that Seattle can gain an advantage and speak to two FAs now while Toronto or Riga, even if they wanted to make a similar trade, would have to wait 2-3 days.
Meanwhile, the counter-argument is "oh but we're so bored, sim all the games today, and let's start the off-season". How about suck less?