If the convergence is normal with VHF antenna or video input, convergence circuit is OK.
If convergence problem becomes visible when you switch to HD input, the convergence needs adjustment for that size or picture mode. Sony TV has different memory data for different size or format pictures.
If adjustment in the customer convergence adjust screen is not satisfactory, someone has to enter the service mode and adjust. Not recommended for rookies.
The game box or any other input will not damage or stress the TV if the game box is working normally.
If convergence is not correct in all size modes and can not be adjusted
you need a repair to the convergence circuits.
Occasionally the convergence ICs are on the verge of failure from accumulated AC power bumps or lightning pulses on the AC line.
A small spark from poor grounding or static electricity can occur when connecting an input and the TV is powered on. Semiconductors (transistors, diodes and ICs) that have accumulated junction damage may fail when the effect of the arc is applied to the junction of the semiconductor.
The failures are often blamed on the Game or other external device. The TV would probably have failed in a short period of time with normal operation.
Turn off power to TVs and external devices when connecting or disconnecting video, audio or antennas. It is also important to use power sockets correctly. All electronic equipment has polarized plugs or 3 prong plugs to make sure the grounding is correct. Using multiple extension cords that are not grounded correctly or incorrect house wiring causes ground loops and unexpected problems. Best is a power bar with 3 prong plug in the wall. easyab