The mistake here is having 2^16 valid options.

If you truly do have 2^16 valid and distinct behaviors, it is not possible for humans to correctly write 2^16 different code paths anyway.

More than likely, the majority of the combinations of your 29 Boolean flags are invalid. You should strive to have that checked by the program, and not only as a note in external documentation.

No one is saying int should be turned into an enum.

You only have 20 options, but making that many distinctive options is not exactly a stretch. It's not like every single set of options is its own code path, most options represents a small deviation at one particular part of the code. Most of the options aren't mutually exclusive either, only a few combinations are illegal.

Imagine a simple shipping system for example. The package might be routed via truck, boat, plane, pipeline, foot, etc... Probably even a combination of those options. The package might be low, medium, or high priority, although high priority packages are not allowed to be delivered by boat. The package might be small, large, or liquid, but liquids can't be delivered by foot. There are 195 different countries with even more regulatory regimes to consider, some of which may have different customs requirements based on mode of transport. Now imagine a problem that is actually complicated.

The idea of encoding all of this business logic into the datatype is a road to madness IMHO. Especially if the rules can change on you and require you to rework your datatypes to match. On the small scale this makes a lot of sense and is good advice, but strict adherence is impractical.

The parent is discussing a situation where you have 16 distinct, binary states many but not all of which are mutually compatible. So you can have 16 bit vector of the states, 16 binary variables or an enum of valid states - the enum would have O(2^16) members because of the distribution of valid states but unlike the others, an invalid state would not be possible to represent.