Yep sounds like he was pushed. There is an article in The Times where they basically said the board told him to walk or they would fire him.
The appointments of the Director Of Football from Barca and the Scout / Head Of Recruitment from Dortmund were quite clearly strategic moves made by Gazidis to remove the remaining bits of power away from Wenger aside from managing the team.
I do think that the likes of Gazidis have been sounding out possible replacements all season hence all the rumours etc.