Can I control two coreless DC motors using L293DD SMD IC?
Can the L293DD SMD IC be used to control these motors?


Yes


  Is there an alternate solution/circuit/IC which can minimize the size and area?


Any of the more modern MOSFET based H-Bridge drivers that exhibit far less loss than the antiquated l293d


  Are ESCs required for these small coreless motors? 


No


  Can they be controlled directly via the L293DD (like normal motors)?


Yes

The L293 is old and, well, basically crap. For efficient battery based operation you realy need to be looking for something a little more modern and efficient. There's length to choose from - take a look on your favourite electronics supplier (which means not Amazon...)