Gamma causes shallower trees (or, at least, trees with fewer leaves), by restricting when splits will be made.
I think the tutorial isn't entirely clear/accurate. For example, the bullet point immediately before the one you're questioning states that gamma penalizes large coefficients, which is not the case (alpha and lambda penalize coefficients, gamma just penalizes the number of leaves). And further down, alpha is the L1 penalty on weights, but the weights are those at each leaf, not on individual features, so alpha does not perform feature selection in the same way as Lasso. (I suppose, though I haven't seen it discussed, that it could force a split candidate's leaf coefficient to zero, causing the algorithm to pass over splitting that feature, perhaps in the long run skipping the feature altogether?)