Yii2 has started using PHP 5.4's Short array syntax. Your error creeps up because of:
spl_autoload_register(['Yii', 'autoload'], true, true);
in Yii.php, which is the new short array syntax. As you have already figured out, you need to install PHP 5.4 now to run Yii2 apps.
The commit which made the changes to short array syntax.
The docs and composer details that have been changed.
The discussion where the decision to move to PHP 5.4 was made.
As Yii2 is still in heavy development, its requirements are also changing. So be sure to read the readme thoroughly before installing.
See also the Backward Incompatible changes list for PHP 5.4, to make changes to your existing code.