Did I get offered a job and accept without really knowing?

I interviewed for a job almost 2 weeks ago. I asked the interviewer when I would hear back and he said, "Honestly we would be happy to have you. I just need to check your references but I am sure you will check out fine. The job starts this day and you should get a call about paperwork soon to fill out. Are you excited?" I remember not being sure what to say because I didnt know if I wanted this specific one yet but also didnt want to rule it out so I said "Yeah sounds great, thanks." Well he has never contacted me since with an official job offer or to fill out any paperwork. I haven't signed anything or made anything official at all...and I don't even know if he has called my references yet.
I ended up interviewing for a different job recently that I liked better, got the official job offer call, and accepted it today.
Now I am thinking back to the first job I applied for and am confused...did the interviewer basically already give me the job..? Should I politely call or email him to tell him I accepted another job offer? Some people I know who I asked advice from said I shouldn't tell the other job that I accepted another job offer because they never officially offered me a job on the first place. Any advice?