Yamaha Cygnus 125 Bj 2007, broken? Help

Hi, I bought me a Yamaha Cygnus 125 bj 2007 3 days ago, checkbook maintained only 7500km. Lief impeccable 80km (overpass), there she also jumped great, demonstration, test drive etc. Seller said still battery is flat, he had it charged and started, interstops etc. was no problem at the home ride. Yesterday I wanted to turn a small round, battery was dead no advertisement, got it then with the kickstarter for my first kick attempts, quite easy and fast Today I wanted to kick it again, didn’t go any more. I removed the battery and kicked it again without a battery, went on… (know that from my old 80s and there should be no damage…) Battery went in again, nothing more. Battery again charged and see even in the Youtube video (didn’t know how to help me than to upload it there ) https://youtu.be/wgcmZ8RQU-o What can it be, starter in ***? For help mega thankable…. Sam