"Her house has two floors."
If 层 is the measure word then the sentence is missing an object. My understanding is that in this sentence 层 which means floor is the object, it can't be both the object and the measure word. If 层 is intended to be the measure word, then the sentence should be something along the lines of 她的家有两层楼。 with 楼 being the object .
The object is actually 层 not 家. also the object wouldn't come before the measure word.
If by "meaning being the same" you mean the listeners ability to decipher the speaker’s intent, then I agree that they’re the same. However, the sentence as is sounds odd and is likely grammatically incorrect. If I said “The house of hers two floors have” the average English speaker would get the meaning of that sentence, however it sounds odd and is grammatically incorrect.
Would appreciate input from native speakers on this.
Yes, as with many DL sample sentences, this one sounds a little unnatural and may seem confusing to some learners. Try look at this way, how many stories does her house have? 她家有几层？The answer is 她家有两层. As to the counter 层, a building can be referred to as XXX(number)层, for example, a 63-story skyscraper in Guangzhou, China is also known as 63层. Native here.