IIUC, it does have code generation—the ability to generate strings at compile-time and feed them back into the compiler.
The argument that the author of TFA is making is that Zig’s comptime is a very limited feature (which, they argue, is good. It restricts users from introducing architecture dependencies/cross-compilation bugs, is more amenable to optimization, etc), and yet it allows users to do most of the things that more general alternatives (such as code generation or a macro system) are often used for.
In other words, while Zig of course didn’t invent compile-time functions (see lisp macros), it is notable and useful from a PL perspective if Zig users are doing things that seem to require macros or code generation without actually having those features. D users, in contrast, do have code generation.
Or, alternatively, while many languages support metaprogramming of some kind, Zig’s metaprogramming language is at a unique maxima of safety (which macros and code generation lack) and utility (which e.g. Java/Go runtime reflection, which couldn’t do the AoS/SoA thing, lack)
Edit Ok, I think Zig comptime expressions are just like D templates, like you said. The syntax is nicer than C++ templates. Zig’s “No host leakage” (to guarantee cross-compile-ability) looks like the one possibly substantively different thing.