@stickysara The answer is... maybe. I would be mildly surprised, but not shocked, if your laptop's thermal paste were so dried out that it absolutely needed to be replaced. Laptop manufacturers know that their products could be used for a number of years and generally prepare for that possibility, and Asus generally makes quality products. It's much more likely that dust clogs a fan or a vent, or something else prevents the fan from spinning properly, before the thermal paste itself fails. On the other hand, it's far from impossible—it would happen eventually, and maybe your laptop's thermal paste just dried out ahead of schedule.
The other consideration is whether you want to invest this kind of money in your laptop. A professional cleaning is usually relatively cheap, but having someone take apart the laptop and apply new thermal paste probably wouldn't be. It would still likely be cheaper than a new laptop, but on the other hand, a decent new laptop would be significantly faster, and if you're going to get one in the near future anyway, you might not want to spend so much on this one. This is where I can't tell you the right answer because I don't know your budget or what your local shop would charge, so think about what you want, and call around to get some estimates.
And of course you can't know for sure that the thermal paste is the issue until someone checks. I'd still try a cooling pad or fan, and borrow one from a friend to test if you can, to see whether you can keep the processor below 95º C while playing. A max in the low 90s is fine and shouldn't trigger thermal throttling. You can also upload an hwinfo log for me to look at if you want.