If the paper would not have used this clickbait title, it would probably go unnoticed and noone would pay attention? Sad truth about sensation-oriented modern lives :(
It is true that MLPs are classic, but the regularizaton methods that apparently make a big empirical difference at this paper are new concepts (data augmentation, skip connections/residual blocks, dropout, batch norm, lookahead, stochastic weight averaging, etc.). They compare againts a good old MLP without the bells and whistles at Table 2 and the classic MLP is quite a poor performer (XGBoost beats a classical MLP very significantly). Which leads to the conclusion that we need all these recent deep learning advances on innovative regularization techniques to make the difference.
Batch norm has an advantage for iterative methods on mini-batches, while XGB uses the full training set. Using batch norm on the full training set is equivalent to Z-normalizing the features, which has no effect at all for XGB as the scale of features plays no role at the split decisions of the tree nodes. Apart few non-parametric data augmentation methods (notice adversarial augmentation is also nn specific), I do not think any other regularization used in that paper can be directly/intuitively applied to XGB.
I agree with your point, e.g. data augmentation can be added, but thats pretty much it. All the other regularization techniques they use are neural network specific and cannot be applied to gradient-boosted trees. What I find particularly striking at this paper is that their method trains a single neural network which outperforms an ensemble of decision trees (XGBoost). Asking for perfect apple-to-apple comparisons means also comparing an ensemble of the MLPs vs. XGBoost. In this context, at least the message here is that XGBoost and/or other gradient-boosted methods are not anymore a silver bullet for tabular datasets. Boosting for trees was great in reducing both bias and variance, but apparently neural networks can achieve the same effect with a high capacity (low bias) and a mix of modern regularization techniques (low variance).
After reading the paper I believe they do both aspects that you mention: i) they give XGboost and all the baselines up to 4 CPU days of hyperparameter optimization time on 20 CPU core servers per dataset, same compute as the author's proposed method. ii) the search space for the XGBoost hyperparameters includes low eta (starting from 0.001) and large num_round ranges (up to 1000 trees) in Table 5 at the appendix.