The standard C library does not have a strtoint32().
I want to convert a string ... to a 32-bit int.
  I know of strtol and strtoimax, but these seem to return 64-bit ints.
There is long strtol() that certainly meets OP's needs.  It forms an integer at least 32-bits.  Use it and additional tests if needed.
#include <ctype.h>
#include <limits.h>
#include <stdint.h>
#include <stdlib.h>
// really no need for this:
// typedef int32_t Int32;
// Int32 strToIntValue(char* str) {
int32_t strToIntValue(const char* str) {
    char* end;
    errno = 0;
    long num = strtol(str, &end, 10);
    if (num == end) {
        printf("No conversion error!\n");
        return 0;
    }
    #if LONG_MAX > INT32_MAX
    if (num > INT32_MAX) {
      num = INT32_MAX;
      errno = ERANGE;
    }
    #endif 
    #if LONG_MIN < INT32_MIN
    if (num < INT32_MIN) {
      num = INT32_MIN;
      errno = ERANGE;
    }
    #endif 
    if (errno==ERANGE) {
      printf("range error!\n");
      return 0;
    }
    // Maybe check for trailing non-white space?
    while (isspace((unsigned char) *end) {
      end++;
    }
    if (*end) {
      printf("Trailing junk!\n");
      return 0;
    }
    // else {
    return (int32_t) num;
    //}
}
Consider printing error output to stderr rather than stdout.
        // printf("range error!\n");
        fprintf(stderr, "range error!\n");
See Why is there no strtoi in stdlib.h? for more ideas.