Laptop emits burning smell after heavy task

Take the laptop to Apple or an Apple Authorized Service Provider to be examined.

If you game hard, you really need a gaming computer and I do not see Mac laptops as being that. Intense games make a lot of heat, that's normal. Unless the Macbook Pro is the Pro or Max option, it has but one fan.

Air intakes on a M-series Macbook Pro are not obvious but cannot be ignored. They are low on the side of the case where the bottom cover contacts the chassis:

ANY blockage, even partial, will result in higher internal temps.

The entire hinge area is the exhaust vent. Blocking any part of that area means more heating.

This all means you must not use your Mac on your lap, a blanket, or a pillow. All with compromise your computer's abulity to keep itself safe.

Apple's comments on the subject:

Keep your Mac laptop within acceptable operating temperatures - Apple Support

In or out of warranty you can get a free over the counter 'Apple Service Diagnostics' test /assessment

Make an appointment for a "hardware issue"

Genius Bar Reservation and Apple Support Options - Apple

Outside the USA

Contact Apple Support - Apple Support

Local USA—

Store List - Apple Store - Apple

Around the World—

Choose your country or region - Apple