Is It Safe to Build a Gaming PC Without Grounded Outlets?

You really just need a UPS. Using a surge protector with a UPS is normally not needed and can actually be unsafe; daisy-chaining them can cause fire risks. The UPS itself should be sufficient to protect your setup and help prevent unexpected shutdowns.

Using a UPS or a surge protector won't solve the issue of having ungrounded outlets. It's definitely something to be cautious about, but it won't necessarily damage your PC by itself unless there's a significant electrical issue.

The necessity of grounded outlets can vary by location. For instance, I've been using ungrounded outlets here in The Netherlands for years without any problems. Personally, my experience has been great with gaming PCs, even without grounding.