Zig is a C-like language that isn't memory safe. A UAF bug looks the same as it does in C where you manually call the allocator to get a block of memory, manually free it, then try to perform an access via a pointer to it.
But I think this page may be overstated? Again: I don't know anything about Zig, but I sure know how a UAF bug works. :) And it doesn't look like Zig is meaningfully susceptible to them? You an crash a Zig program with a UAF, but the actual vulnerability wants more than the crash: it wants the program making uncontrolled writes to live memory used elsewhere in the program, which is a condition I don't think is present in Zig as it's being described.
If that's the case, that bodes poorly for the claim that Zig is susceptible to C/C++-style double free vulnerabilities, too.
It would be genuinely weird to see a new language rolling out that had C/C++'s UAF problem.
(As was pointed out elsewhere: if you're using an external allocator, or the `c_allocator`, all bets are off. But so is unsafe code in Rust, I guess?)