Praise be to Allah.
There is no difference between reading the Quran from the Mus-haf or reading from an electronic Mus-haf, or from pages on the Internet, or from the screen of a mobile phone . What counts is reading, moving the lips and looking at the written words of Allah, may He be Exalted, and all of that is achieved when reading from an electronic screen. So it attains the reward of reading concerning which the Messenger of Allah (blessings and peace of Allah be upon him) said: “Whoever reads a letter of the Book of Allah will have one good deed for it, and the good deed is multiplied tenfold. I do not say that ‘Alif-Lam-Mim’ is one letter; rather Alif is a letter, Lam is a letter and Mim is a letter.” (Narrated by At-Tirmidhi, 2910. classed as authentic by Al-Albani in Sahih At-Tirmidhi)
It says in Al-Mu‘jam Al-Wasit (2/360): “Reading the Book means following the words with the eyes and uttering them.”
Shaykh Al-Islam Ibn Taymiyah said in Al-Fatawa Al-Kubra, 2/419:
“If he reads the Quran for the sake of Allah, may He be Exalted, then he will be rewarded for that in all cases.”
With regard to the question of whether Wudu is required for this reading, being in a state of purity is not essential for reading Quran, rather it is only essential for touching the Mus-haf, because the Prophet (blessings and peace of Allah be upon him) said: “No one should touch the Quran except one who is in a state of purity.” (Narrated in the Muwatta’ of Malik, 468; classed as authentic by Al-Albani in Irwa’ Al-Ghalil, 122)
If one who had memorised it recites it, or if it is read from the Mus-haf without touching, there is nothing wrong with that.
Based on that, there is nothing wrong with reading Quran from the computer screen without Wudu , because this is not touching the Quran ; rather it is like reading from the Mus-haf without touching, just like if the Mus-haf is open in front of one and one reads from it without touching it.
And Allah knows best.