2012 GP, not the inaugural race. Also the situation was a bit more complicated. The stakes were high. On a number of levels. Mclaren's strategic partnerships- trade, ownership and sponsorship (Vodafone)- were finely balanced on its decision to race in Bahrain. F1's reputation hanged in the balance. Jean Todt's and Ecclestone's position of power going forward was centered on the race going ahead; they'd nailed their colours to the mast having accepted Bahraini influence and money, respectively, in their respective organisations. Were the race to have been cancelled, following its cancellation the year before, it would've been banned from the calendar for a set number of years per FIA rules. Dennis reportedly sought not only for the racing team to miss the race but to push for its cancellation. He was in effect calling a no confidence in Mclaren's ongoing relationship with Bahrain; he was angling to sever the Bahraini's influence and, ultimately, ownership of the organisation.
The vote was important, then; it was not a vain quibble. A decision by Mclaren not to race presented potential for other teams to decide in turn not to race; and would have publicly called into question the FIA and FOM decision to race, regardless. There being a very real possibility of such a scenario- where the race would most certainly have been cancelled- would have been a pr disaster for the ruling Bahraini regime; it used F1 to present the kingdom as a place of business and not as the place of brutal repression, civil unrest and human rights abuses that it was/is.
So over at Mclaren in the immediate weeks prior to the scheduled race (about two and a half), a board meeting comprised of the shareholders- Dennis, Ojjeh and Mumtalakat (the investment arm of the kingdom, run by members of the royal family)- was held. Throughout their time at Mclaren, Ojjeh worked to an agreement that he'd vote in lockstep with Dennis; Dennis in effect making the major decisions and determining the company's projectory. It stemmed from since the Mercedes' part ownership of the company; it was to preserve their will over the company. Dennis and Ojjeh would occasionally alternate chairing the meeting; the former normally holding the position. This time Dennis was away on business, Ojjeh represented both men and instead of carrying Dennis' vote forward, he vetoed him.
This was unprecedented; the pact had never been broken before. Voting to overrule Dennis sidelined him and stepped away from Dennis' way of running the organisation. It set about his downfall (given that Dennis' decision conflicted with the majority shareholders, the Bahraini investment company run by the royal family...); it effectively nullified him lest he either audaciously enact a hostile takeover of the companies, buy back in to a majority shareholding or brush Ojjeh aside- all of which he was unable to do. A lot of company policy and direction went against Dennis' philosophy thereafter. This explains Dennis' sudden sacking of Whitmarsh- an Ojjeh ally- during Ojjeh's lung transplant; his attempt at buying out Ojjeh whilst the latter was in ill health; and his in turn being forced out by the Bahrainis and Ojjeh, lest he buy them out within a set time frame.