The 27th July release date is a case of Sony's marketing team employing a gimmick.
In T2, Judgement Day was the 29th August 1997. However, due to the destruction of Cyberdyne's premises in that film, the timeline was altered and Judgement Day was averted, at least temporarily.
In T3, Judgement Day, deemed inevitable, ultimately takes place on the 25th July 2004. Hence the release date of the 27th July 2015, ie the Monday closest to its anniversary!
It's probably a case of Sony being too clever for its own good since the significance of the date will probably be lost on most people, due to T3 not having the acclaim or love of its two predecessors. It might be a case where bringing the release date forward to the beginning of July, to cash in on the theatrical release of Genisys, might actually generate more sales for them.