The only difference between X3D just has more L3 cache than non-X3D chips. The 3D vertical stacking is just how AMD manages to fit it on the package. It's nothing special otherwise.

Cache is used to accelerate CPU operations because cache is orders of magnitude faster than even system RAM, but it's also far more limited. Even the 9800X3D which has more than most any other consumer CPU on the market has only 96MB, whereas you might have 16GB or more of RAM. That means not everything is going to be in cache ever, so you're relying on cache hits, where the data the CPU needs just happens to have been used before (to become cached) and still exists in cache. Having more cache simply increases the chances of getting a hit.

Games are one particular workload that tends to reuse the same data across multiple CPU operations, so it makes it a good candidate to be accelerated by cache, and having more cache means you generally get more benefit. There's two important takeaways here: 1) games only benefit in as much as they are reusing data that is cached and 2) having less cache doesn't necessarily mean worse performance.

That last one is where people go off the rails. Benchmarks that show X3D chips demolishing everything else are intentionally creating CPU bottlenecked scenarios to tease out the differences between the CPUs. That's fine and what should be done in a proper CPU review, but it doesn't necessarily represent real world performance. If you don't have a CPU bottleneck, then there may not actually even be a difference, because that extra bit of performance the CPU can squeeze out from having more operations directly using cache doesn't come into play. Non-X3D chips also have cache, and the amount of cache they have may also already be enough. In short, X3D doesn't guarantee better performance. It just gives you the potential for better performance.