The second algorithm referred is the linear booster. In that case, the base learner is an elastic net regression (i.e. a linear model with $L_1$ and $L_2$ regularisation). Regularised regression methods are sensitive to feature scaling. They need features to be on similar scale; otherwise, if the features are on different scales, we risk regularising a particular feature $x_1$ far more (or less) than another feature $x_2$ for the same regularisation pair values $(\lambda_1^*, \lambda_2^*)$.
Strictly speaking, tree-based methods do not require explicit data standardisation. XGBoost with a tree base learner would not therefore require this kind of preprocessing. That said, probably it will help numerically if the data themselves are not too large or too small values. In the end of the day, certain gradient calculations are done. Having values closer to unit scales instead of billions (or nanos) is more convenient; numerically the whole system is more stable.