How does a veggie-less diet affect the human body?
There is a list of several implications of not eating vegetables (references 1, 2, 3):


Weight gain (by eating fat-rich products);
Malnutrition (not reveiving enough vitamin A, C, D, K, etc);
Digestive problems (low fiber intake leads to digestion disorders, which could lead to health problems);
High risk of heart disease;
High risk of certain cancers.


I also pulled up the nutrition fact sheets for vegetables, fruits, and seafood created by the US Food and Drug Administration.

In order to obtain all the necessary vitamins, one can substitute vegetables for fruits. For example, to obtain 100% of the daily value of vitamin A, one should eat as little as one carrot a day. In order to get the same amount of vitamin A from fruits, one should eat 134g of cantaloupe, or 462g of grapefruit, or 50 large apples a day. Although this could be difficult but possible, the sugar content of the above-mentioned fruits should be taken into account.

Something else which needs to be considered is that vegetables are richer in minerals (iron, potassium, calcium), compared to fruits.

All this in mind, perhaps all minerals and vitamins could be acquired from a source other than vegetables.