Advise severely needed! SOS

So, I'm recently getting the hang of this casual dating thing, I got dumped, a 2 year relationship, and decided to try the whole casual dating thing. I went out a few times had a few hookups but I wasn't happy and that's not what I wanted. I wanted something more. Then, one day out of boredom I got back on tinder for the first time in a while and saw that I was superliked so we started talking and he seemed like a decent guy and wanted an actual long term relationship like me, not just casual. We talked for a long time and he CALLED me to ask me out on a date. Like a real date not a "chill hangout sesh". So we go out on our first date and I accidentally say the word "dating" and he's like "is that what you're calling this?" And I asked him what he wanted to call this. He said he'd consider it seeing each other because we aren't exclusive (well I was exclusive to him but I didn't know he wasn't exclusive with me) he tells me he's seeing two other girls. So do I continue to see him and fight for attention hopefully making a long term relationship out of this and if so how do I get him to be exclusive. Or should I just not worry about it and walk the other way?