Do I need a pure sine wave UPS for this gaming PC?

Pure sine wave is more of a compatibility precaution than an absolute requirement here. Many people run modern gaming PCs on simulated sine wave UPS units without issues, but if the price difference is small, I’d choose pure sine wave rather than gambling on compatibility. Also, the UPS should be sized for the real load and used mainly to shut down safely—not to keep the PC gaming for a long time.

Your PSU should probably handle a simulated-sine-wave UPS without trouble. If a pure sine wave model is only slightly more expensive, though, the extra cost can be worthwhile for peace of mind—especially since you regularly deal with blackouts and storms. Make sure the UPS has enough capacity for the PC and monitor, and check its actual watt rating rather than relying only on the VA number.

Given the frequent outages and surges you described, a good UPS makes more sense than it would for someone who rarely loses power. A quality surge protector is still useful, but it won’t keep the computer running or protect against every kind of power problem. Choose a reputable unit with replaceable batteries and enough headroom for your system.

A pure sine wave UPS isn’t strictly required for this system. Modern, decent-quality power supplies usually work fine with simulated sine wave output, and problems are relatively uncommon. The issue mainly matters when the UPS switches to battery during an outage, not during normal operation.