I would like to know if it is permitted to use a digital Holy Quran for recitation, reading and such-like, as the one shown in the below video:
Yes, it's allowed, as long as you trust that there's no distortion.
Allah says in Surat 'Āli `Imrān:191:
This ayah talks about "those who understand" in the ayah preceding it. The idiomic meaning of the expression "قياماً وقعوداً وعلى جنوبهم" is in any case and way.
There's a very essential rule in Fiqh that says:
That basically means that a new thing is allowed unless it's contradictory to an existing rule.
Quran originally wasn't revealed in any physical form (unlike, for example, the panels of Musa -pbuh-), it was revealed gradually and the prophet and Sahabah memorized it, then later in the Time of Rashidi Khalifates, it was paper-written because many of the Sahabah who memorize it died, and so original "memorizers" are getting fewer.
Then, when printing became easy, prints of Quran entered every house to enable normal people to read and understand Quran, since the majority doesn't memorize it.
Any way that is intended to help people read Quran and understand it is very welcome, and the effort is thankful, Mufassireen tried to make Quran clear, their efforts are thankful, printers tried to make Quran books (mushaf) available, their efforts are thankful. And now comes technology time, and efforst are always welcome.
It's very welcome to try to digitize Quran so people can read it easily in, say, the Bus, the Metro... etc. It's very welcome to digitize it so search and research becomes easy (and we're being benefit from that here).
Allah says in Surat Al-Ĥaj:32:
Trying to make Quran easy-to-read can be included in such meaning.
Is deleting a "Quran.pdf" destroying a copy of the Quran?
In addition to Ansari's comment, I would like to say that if you do that with a bad intention then you're sinful, else you're not so long as you do that in a respectful way. Muslims do destroy copies of Mushaf and there's no problem in that so long as they do that in a respectful way, there are preferred ways to do that, of course.