I think you're misreading this statement:
For example, many modern 3-D Games have their high performance core engine written in C++ and Assembly.
Games (and most programs these days) aren't "written in assembly" the same way they're "written in C++". That blog isn't saying that a significant fraction of the game is designed in assembly, or that a team of programmers sit around and develop in assembly as their primary language.
What this really means is that developers first write the game and get it working in C++. Then they profile it, figure out what the bottlenecks are, and if it's worthwhile they optimize the heck out of them in assembly. Or, if they're already experienced, they know which parts are going to be bottlenecks, and they've got optimized pieces sitting around from other games they've built.
The point of programming in assembly is the same as it always has been: speed. It would be ridiculous to write a lot of code in assembler, but there are some optimizations the compiler isn't aware of, and for a small enough window of code, a human is going to do better.
For example, for floating point, compilers tend to be pretty conservative and may not be aware of some of the more advanced features of your architecture. If you're willing to accept some error, you can usually do better than the compiler, and it's worth writing that little bit of code in assembly if you find that lots of time is spent on it.
Here are some more relevant examples:
Examples from Games
Article from Intel about optimizing a game engine using SSE intrinsics. The final code uses intrinsics (not inline assembler), so the amount of pure assembly is very small. But they look at the assembler output by the compiler to figure out exactly what to optimize.
Quake's fast inverse square root. Again, the routine doesn't have assembler it it, but you need to know something about architecture to do this kind of optimization. The authors know what operations are fast (mulitply, shift) and which are slow (divide, sqrt). So they come up with a very tricky implementation of square root that avoids the slow operations entirely.
High-Performance Computing
Outside the domain of games, people in scientific computing frequently optimize the crap out of things to get them to run fast on the latest hardware. Think of this as games where you can't cheat on the physics.
A great recent example of this is Lattice Quantum Chromodynamics (Lattice QCD). This paper describes how the problem pretty much boils down to one very small computational kernel, which was optimized heavily for PowerPC 440's on an IBM Blue Gene/L. Each 440 has two FPUs, and they support some special ternary operations that are tricky for compilers to exploit. Without these optimizations, Lattice QCD would've run much slower, which is costly when your problem requires millions of CPU hours on expensive machines.
If you are wondering why this is important, check out the article in Science that came out of this work. Using Lattice QCD, these guys calculated the mass of a proton from first principles, and showed last year that 90% of the mass comes from strong force binding energy, and the rest from quarks. That's E=mc2 in action. Here's a summary.
For all of the above, the applications are not designed or written 100% in assembly -- not even close. But when people really need speed, they focus on writing the key parts of their code to fly on specific hardware.