Suppose I meet a non-Muslim on the streets, I greet him and we both start a conversation, is it obligatory for me to invite the non-Muslim towards Islam?
It's an individual duty for a Muslim to do Da'wah. But that differs case by case. Allah (ﷻ) said, "invite to the way of your Lord with wisdom" (16:125). Every situation is different and you should respond in a wise way. Perhaps at times someone is receptive enough for you to just straightforwardly invite them to Islam. Perhaps at other times, they are not and you need subsequent talks with them before you get to that stage (e.g, atheists who don't even accept the basic premise that God exists). So work your way to that, inshaAllah.