I think it was neither playful nor malicious, at least as I understand the word "malicious."
I think Nixon was under a great deal of strain, and lost his temper with Ziegler, whom I believe Nixon actually liked. He was at the time only 29 years old, the youngest press secretary in history IIRC.
Also, contrary to the image painted of him by the MSM over the years, Nixon was not an ogre, not a mean man, not a hateful man.
I think the "shove" of Ron Ziegler was simply an emotional outburst by a man under tremendous pressure.
What Nixon did was very bad, and he shouldn't have done it. He should have fired the Watergate people and allowed the legal system to punish them, although with the MSM being what it is that very well could have ended his Presidency anyway, IMHO.
But the Democrats basically wanted to conduct a show trial against him, as was demonstrated by Hillary Clinton, who wanted to deprive Nixon of his right to council.
If they could have, some Democrats would have liked to see Nixon executed by hanging in the Rotunda.
The hippies who were worming their way into the lower echelons of the Democrat party at the time would have loved that. They hated Nixon with a passion, but the older Democrats were a bit more sober.
Difference is that today, the entire Democrat party — from most junior to most senior — hates DJT with a murderous intensity. Some have even said so publicly.
Trump has pretty much everybody in the media and establishment against him, hoping that he fails so that they can say they told us so and go back to business as usual.
For that reason, I'm giving Trump every benefit of the doubt and I'm not joining some of my fellow Freepers in condemning him because he is trying to get things done by working with this pond scum that we have in Washington (i.e. Ryan). With respect to Congress, Trump needs to play the hand he was dealt and it's up to the people to change the composition of the House and Senate come 2018 to make things easier for Trump to get his agenda through.