What could I use for this Yakisoba dish instead of cabbage?
From a purist perspective, cabbage is fairly important to the recognizability of the dish by that name (as well as the pickled matchstick-cut ginger). Additional ingredients beyond those two are far more substitutable (at least from common Japanese perspective); the cabbage actually contributes a fair amount of flavor to an otherwise unremarkable dish. In fact, the presence of a mere two leaves suggests to me this is a pretty small portion.

So here's a "how to avoid substituting" answer, followed by a how to substitute answer.

Cabbage tends to survive a good 2 weeks in the refrigerator, so I wouldn't fret about it too much. It also makes a good garnish, shredded; additionally, it was super trendy for a few years for izakaya in Japan to serve raw cabbage with miso paste (sometimes sweetened). I know many shops that will even sell a half a head (in Japan it's easy to buy even a quarter head of cabbage), or you may find a small package of pre-chopped, unseasoned coleslaw mix, which typically contains cabbage and carrots. Finally, cabbage makes an excellent foundation for a vegetarian soup stock, so it's great way of making sure any surplus doesn't go to waste.

The only substitutes somewhat consistent with the style of the dish are other variations of cabbage (bok choy, napa cabbage, possibly kimchi) or certain crispy roots like kohlrabi. But frankly, those steer the dish into a non-Japanese style of pan-fried noodles. Not that there's anything wrong with that, but the texture and flavor differences are fairly pronounced. In a pinch, we've made these substitutions in my home, but in that case it was more about using up available ingredients, rather than trying to find an alternative.