Is it a requirement? Well, I don't know of anyone who was successful that didn't eat as many veggies as they could.
They fill you up, aid in health, and make less room for the things that tripped you up in the first place (like bad carbs and processed foods).
To be successful, I'd recommend that you have veggies with breakfast, lunch, and dinner, and then with at LEAST one of your snacks.
That said, if you are working off of a cheat sheet for this plan, you're going to have trouble...
like all diets, you will be
most successful if you
read the book. If you can't afford it, check your local library--most, if not all, carry it. The information in the book is indispensible to help you make decisions about your eating and to understand why things are or aren't allowed/suggested. It looks large, but at least half of it is food lists and recipes, so it doesn't take long to read.
You might try putting your calories into fitday (
www.fitday.com) to find out how much you are eating a day. If your other meals are as small as your breakfast, you may be eating less than 1200 calories a day which can stall your weight loss too. It's too little...make sure you eat at LEAST 1200 a day, okay?