This looks like the power supply is repeatedly restarting. Without load and no output overload, this is hard to see at the output, so you should check if the supply is restarting at no load also. Connect the scope at the secondary side, directly at the transformers pins to see if it is cycling or running stable.
Restarting can be due to output overload or some protection circuit kicking in. If the power supply cycles without load, one might suspect a defective output rectifier diode, maybe just an capacitor (often a small one on the primary side) lost its capacity or an faulty optocoupler. The controller chip and the main power components appear to work.