This table is representing the conditional probabilities $P(g^1|i^0, d^0)$, and others like that. Let $X$ represent $i^0,d^0$ for convenience. Adding the first row, we have $P(g^1|X)+P(g^2|X)+P(g^3|X)=\frac{P(g^1\cap X)}{P(X)}+\frac{P(g^2\cap X)}{P(X)}+\frac{P(g^3\cap X)}{P(X)}=\frac{P(X)}{P(X)}=1$, because $g^1, g^2, g^3$ are disjoint (no two can happen at the same time) and their union is everything (one of them must happen).
If we tried to do the same thing with the columns, we would get a similar situation in the numerators, but the denominators would now be all different, so the fractions couldn't be added in the same way.