Can I be admitted into a PhD program with non-thesis MS degree?
It depends on the university. Some Ph.D. programs have extra requirements for students who did not complete a thesis (or they will not accept these students). Others are fine with a 'capstone/directed project' which has elements of a thesis. Others may simply ask that students who did not complete a thesis take the GRE for admission into the Ph.D. program while not requiring this for students who did complete a thesis (I attend an R1 university in the US and this is the case here).

So the answer is yes, but it depends on the university.