Masters w.o. thesis on the area I'm interested vs. masters w/ thesis on a different area
Should I accept him and try to write a thesis alone or look for a different adviser on a different area?

This is up to you. You are pursuing a graduate degree and you have to take charge of your educational path. You have to weigh both options. A) Writing a thesis alone with no supervision and potentially having to struggle, B) Working under a different adviser who will supervise you, but it may be a boring/uninteresting topic. 

Is it important to have a masters degree with thesis to apply for a PhD program?

This is dependent on the program. Some programs are more research heavy than others. I would scope out your future plans and tentatively look at what PhD programs you would like to apply for and see what their requirements are. I do believe that it is impossible to do "too much" work when applying for a PhD program, so a thesis may be in your favor.