I don't know anything about the history of blue LEDs, but I will convert some comments into an answer. (Thanks to Conifold for some links.)
The Nobel committee's deliberations are kept secret for 50 years (Statutes of the Nobel Foundation, § 10), so any answer before the year 2064 can only be speculation.
"In no case may a prize amount be divided between more than three persons" (§ 4), so when there are more than three people deserving of a prize, they have to stiff someone. That happens fairly often, and it probably did happen in 2014. Wikipedia says in its list of Nobel Prize controversies
The 2014 Nobel Prize in Physics [...] did not recognize the decades of incremental work in developing the LED by other pioneers such as Oleg Losev, Nick Holonyak, and Gertrude Neumark and overlooked a prior claim for invention of the blue LED by RCA materials researcher Herbert Paul Maruska.
and Moustakas isn't even on that list.
The tweet quoted in the question (suggesting Moustakas deserved the prize) was not by a physicist or engineer, but by the managing director of Boston University's Office of Technology Development, which was at the time suing to enforce a patent of Moustakas's related to blue LEDs. Wikipedia's only source other than statements by BU seems to be a MetaFilter post by user bolix, who claims to have been on the jury of one of the patent cases, which decided in BU/Moustakas's favor. Bolix suggested that the existence of that pending case (it was decided in 2015) might have biased the Nobel committee against Moustakas, but it's unclear to me why that would be true. An appeals court seemingly overturned that jury's decision and invalidated the patent (see if you can make more sense of that article than me; it's extremely confusing). Together with the fact that Moustakas's claim to the prize isn't mentioned in Wikipedia's list of Nobel controversies, only in his own Wikipedia article, I wonder if he really didn't deserve it. But as I said I don't know anything about the history of blue LEDs.