Buyer paid for car and took it with him, but no signed purchase contract

Hello guys, yesterday a 20 year old car “sold” for 300€. Here I put it in mobile.de, and after 1min. a foreign buyer called. He knocked after a few dates he wanted to know about me. Then he said that I had received a purchase confirmation by email, which I should answer. So I confirmed this by email and took out the ad. Nnoch on the same day his colleague with the tow truck was there from a county about 150km away. Of course P The guy then telephoned with an Arabic accent a few times with his cell phone and looked under the bonnet a few times, then suspected all possible non-existent damage and phoned around again. A long time later he then pressed the money into my hand and loaded the car. I unscrewed the license plates and kept the car letter to register the car myself. I should then simply send the papers back to me. He didn’t want to have a TÜV and AU report. I just wanted to conclude a purchase contract, when the guy suddenly asked me about the old letter. I affirmed this and went into the house to get him. I didn’t find him right away, but I didn’t come back after about 5min. In the meantime the guy and my car had disappeared. Now it seems funny and a little murky: car away, (real) cash, still all the papers and license plates. in my possession, but no terrible thing, that the car has been in the hands of the guy since yesterday. Do I have to worry about that???