Although NAND gates are universal gates (any combinatorial boolean logic function can be built from nothing but NAND gates), in practice it's usually more space efficient to use a mixture of different gates.
To be fair, it's almost impossible to build anything out of fully discrete components these days. If you use a TO series transistor, you could argue those are also ICs and vacuum tubes/relays aren't cheap or too easily accessible.
Chip photography site zeptobars.com has some photographs of modern transistors, and while some have interesting geometry, I didn't see anything that I'd consider an integrated circuit, i.e. something that would be drawn as more than a single transistor symbol on a schematic.
There are some "discrete" transistors with built-in ESD protection, e.g. NCV8440A, but those are unusual, and under normal operating conditions they work just like a normal transistor so I'd still count them as discrete components.
Transistors in individual packages are called discrete components. Even if they use the same technology as ICs, they're still discrete. You can certainly build useful analog and power circuits with only discrete components. Somebody even made a CPU from them [1] which was a much bigger circuit than TFA's IC video card will be so it's worth distinguishing truly discrete from simple ICs.
So it's clear, a 74xx is just a bunch of NAND gates. Nothing at all higher level than that.