Shinawatra also faced a 32-month long Islamist insurgency in southern Thailand (according to Strategypage, with the most recent terrorist attacks being the nearly simultaneous bombings of 22 banks in the south part of the country. General Sondhi, the man who led the coup, happens to be a Muslim (according to Publius Pundit's source), but it would be premature (to put it mildly) to call this an Islamic or Islamist coup. According to the CIA Factbook, less than 5% of Thailand's population is Muslim.
Publius Pundit has a good compilation of Thailand links. King Bhumibol has considerable influence in Thailand, which is why the new military junta quickly pledged their loyalty to him. Whether democracy or military dictatorship takes hold, it look like it's the king's call. It is a constitutional monarchy, after all.