In Economics “rent-seeking” is seeking to receive a “rent”, but the concept of “rent” here is broader than merelly the kind of rent paid for a property (for example, when banks place themselves in the position to get a commission out of every small financial transaction out there, through “Touch To Pay” schemes, they are “rent-seeking”).
So whilst not all rent-seekers are landlords (probably not even most rent-seekers), all landlords are rent-seekers, which is exactly how I handled those definitions in my post.
Your post is like saying “‘Apple’ is not the same as ‘fruit’” when somebody else whilst talking about apples called them “fruit”.