That's not clear, though. "The new program" it talks about is after running fork and exec, not just exec. It doesn't specify which call resets the pledge.

From the quoted text I'd understand it's the `exec` that resets the pledge.

I installed OpenBSD so I could check this out. tl;dr, you were right.

    $ cat testpledge.c
    #include <unistd.h>
    #include <stdio.h>
    int main()
    {
      pledge("proc exec", NULL);
      execl("/bin/echo", "echo", "asdf", NULL);
      _exit(0);
    }
    $ cc testpledge.c
    $ ./a.out
    asdf

After fork, the original program is still running. The text specifically refers to the proc promise, which allows fork. It may be tersely formulated, but I really don't see how you could interpret this text otherwise.