If voltage and the tip connector are the same it will work, output equals Volts * Amps, stock is 19.5 * 9.23 = 180w, thus the 330w is 19.5 * 16.9. Voltage is the frequency and must match, amps is the amount of power capable of being delivered, that is fine to exceed.

Since it sounds like it only happens after extended gaming, and summer is coming to an end, the problem may resolve itself with cooling ambient temperatures. Make sure the power supply is in a ventilated area and not on something that will reflect the heat back like carpet (prop it up if possible).

I used to have an Asus laptop that would have the same problem back in the day, I actually ended up using a Heatshift laptop pad under it to increase the heatsinking and that worked out for me. Looks like Amazon only has them in pink (lol) right now but it's pretty cheap: https://www.amazon.com/ThermaPAK-Laptop-Cooling-Heatshift-Pad/dp/B002VGQMJE

Works by melting a salt that is a solid at room temp, the phase change absorbs the heat. It will resolidify at room temp or you can throw it in the freezer for 10 min during marathon sessions once all the salt has melted. I just put the pad on the ground with the power supply sitting on top of it