Nintendo's E3 direct having more views than the other directs for the year isn't proof that releasing a video june = more views. The E3 direct has the most views because it is their biggest of the year and expected to be such.
In fact it's remarkable that their other directs are so close to their biggest yearly presentation. If anything I'd take this evidence to show the exact opposite of what you're trying to prove. Their smaller less ambitious directs aren't miles behind their e3 views.
If they hyped a direct as the biggest of the year (as is expected of their e3 direct) rather than just one of several directs I have no doubt they could achieve equal views to their e3 direct at a different time of year in lieu of E3.
The E3 direct had more views due to the actual announcements and public expectations not due to the time it was released. A June release isn't necessary for either high expectations/anticipation nor exciting announcements, it just requires actual hype building which they don't do for their usual directs.
Releasing a video at E3 may be an easy way to cultivate high expectations and a level of importance and thus views, but it is not the only way and it is not necessary.
There is no reason an event outside of E3 HAS to have less views, it depends entirely on how the event is managed and publicised.
But an example of an event outside e3 getting more views...
PS4 Reveal Event (2.8m views) - https://www.youtube.com/watch?v=RiNGZMx2vhY
PlayStation e3 2013 (2.4m Views) - https://www.youtube.com/watch?v=DmoZAPDV3ew
Though just like your example, this isn't proof of anything.
The best example is the PS4 reveal trailer that they released right after the reveal event in Feb.
It went viral for about a week or so after the event. Like I have been saying, this is the internet age. It doesn't take long for info to spread, regardless of where and when it is released.