No it doesn't count as islamic governance. Democracy as a concept and ruling system has its origins in kufr and is based on kufr. Prophet Muhammad (saw) only ruled the people by establishing the Khilafah state and implementing the shariah upon them in totality. Democracy puts what laws to choose to a vote and as democracy stands on pillars of other kufr concepts such as freedom of expression (eg what was published by charlie hebdo), free market policies that also permit the sale of alcohol and gambling etc the list of unislamic bases used upon which democracy stands should be enough to realise that it is completely different and incompatible with the implementation of Islam. What has happened in a few Muslim countries like Saudi is that they pick a few Islamic punishments to implement and say that they are implementing shariah when in fact they're not. Or you get countries like Pakistan that claim to be 'Islamic republic' just cos' they misapply some blasphemy laws but at the same time choose to vote for leaders who allow kufaar troops to set up bases in Muslim lands to bomb other Muslims both in Pakistan and Afghanistan.

What has happened is that the Ummah has lost the true Islamic leadership and ruling system for almost a hundred years, so people are so out of touch with the idea of what an Islamic ruling system is supposed to consist of and are so defeatist assuming it's too hard to make it a reality, that instead they seek a 'compromise solution' in which they implement a bit of islam and a bit of kufr and call it 'islamic democracy'- implement a handful of islamic rules to keep the religious lot happy and let the rest of the laws be based on kufr to keep the real leaders in the white house etc happy. There is no such thing as islamic democracy; there is either democracy or there is islam and anyone trying to reconcile the two is deceiving the ummah into compromising a chunk of islamic values.