In economics 1/3 of 18 studies failed to replicate? A study that small, what are the odds that study itself would replicate? Note that this claim is restricted to experimental studies, which are usually testing human decision-making on economic questions. This is the field of economics closest to social psychology. It seems plausible to me that the model of "get a bunch of people in a room and ask them some questions" is not a reliable methodology.
Economics as a whole may have a problem with replication, but we can't tell from the information on that page. There are whole fields that aren't even mentioned -- no physics, no chemistry.
If your paper in ML doesn't provide code, I assume that it's not reproducible and the authors made a conscious decision to not release the code...
The fields affected have three properties: they deal with complex entities, they are interested in phenomena that is generally investigated using statistical methods and they deal with noisy data. For those fields, we need new methodologies, but other sciences do not have a comparable problem.
Economics, social sciences, even medicine.