Why they are a security feature? They are not, the article even says it. Even if UUID4 are random, nobody guarantees that they are generated with a cryptographically secure random number generator, and in fact most implementations don't!
The reason why in a lot of context you use UUID is when you have a distributed system where you want your client to decide the ID that is then stored in multiple systems that not communicate. This is surely a valid scenario for random UUID.
To me the rule is use UUID as a customer-facing ID for things that has to have an identity (e.g. a user, an order, etc) and expose it publicly through APIs, use integer ID as internal identifier that are used to create relations between entities, and interal IDs are always kept private. That way numeric ID that are more efficient remain inside the database and are used for joining data, UUID is used only for accessing the object from an API (for example) but then internally when joining (where you have to deal with a lot of rows) you can use the more efficient numeric ID.
By the way, I think that the thing of "using UUID" came from NoSQL databases, where surely you use an UUID, but also you don't have to join data. People than transposed a best practice in one scenario to SQL, where its not really that best practice...