Their grammar lacks the crucial component that is the recursive structure of natural languages, which was originally pointed by Chomsky, et al.

Here's how I (Japanese native) would do it:

  SENTENCE = S 。
  S = BUN* verb | BUN* NP be-verb
  BUN = NP pp | adv  (pp = postposition, or 助詞) 
  NP = noun | adj NP | S NP

Warning: this is a highly simplistic version. But this way, things like "今日 築地 で 寿司 を 食った 。 (Today Tsukiji [place-mark] sushi [object-mark] ate .)" could be parsed as follows:

  (S (BUN (adv 今日))
     (BUN (NP (noun 築地)) (pp で))
     (BUN (NP (noun 寿司)) (pp を))
     (verb 食った)) 。

Then, this can be further extended to a compound sentence: "築地 で 食った 寿司 は うまい 寿司 だった 。 (Tsukiji [place-mark] ate sushi [subject-mark] good sushi was .)"

  (S (BUN (NP (S (BUN (NP (noun 築地)) (pp で))
                 (verb 食った))
              (NP (noun 寿司))) (pp は))
     (NP (adj うまい)
         (NP (noun 寿司)))
     (be-verb だった)) 。

p.s. Yoda has nothing to do with this grammar.