Is the interval variable considered as a type of numerical variable or ordinal variable?
This is the formal definition of an interval (from Wikipedia):

In mathematics, a (real) interval is a set of real numbers that
contains all real numbers lying between any two numbers of the set.
For example, the set of numbers x satisfying 0 ≤ x ≤ 1 is an interval
which contains 0, 1, and all numbers in between.

This definition doesn't tell us what to do to represent an interval for ML purposes... and that's normal :)
For ML purposes we need to decide a suitable representation, and there's rarely a mathematically pure or unique way to represent a mathematical object. Your confusion comes from the fact that the sites you mention propose their own representation, i.e. they consider a particular definition of interval, presumably because it suits their goal. The second one in particular is clearly defining an &quot;interval variable&quot; as an object in a particular language, with constraints which have nothing to do with the above definition.
Now to answer your question: an interval is not atomic, since it's not a single value. So strictly speaking it's neither a numerical nor an ordinal.
But you're probably not very satisfied with this answer, since you still want to be able to use this kind of feature. How? As usual, it depends:

Most of the time an interval can be converted to an ordinal value (note that it's a conversion, i.e. we simplify the data to make it usable). The conversion to ordinal is typically done by numbering the possible intervals (following their order) with integers. If the variable is going to be a label in a classification task, it can even be converted to a categorical variable.
However there are cases where an ordinal would not be a good representation, in particular if the intervals are not equal and the ML method involves distances. In such cases it's probably safer to convert the interval to a numerical value, typically the mean of the interval. This way both order and distances are preserved.