Like you, I haven't read the book and got the same impression from this film, that Heathcliff is Earnshaw's son. I missed the bit of dialogue you quote, but I distinctly remember the following lines (which can also be found in the quotes section of the film):

• Mr. Earnshaw: We lost a son, didn't we. Now, thanks be to god, we have another. He can be a brother to them.
• Mrs. Earnshaw: No doubt he is already.

That was the implication in this particular screenplay. I communicated with Patrick Tilley, the writer of this screenplay a few years ago and here's what he said about the matter:
"Emily's portrayal of Earnshaw Sr. reveals a hard, brutal man notably lacking in charity. There seems to be no rational explanation of why such a man would bring an orphan found in
Liverpool into his home unless of course the author simply made it happen to help her plot.
Earnshaw's choice of Liverpool to which (if memory serves me) he had made more than one
visit is an odd choice for a farmer living in Yorkshire. What kind of business was he doing
there? Given the physical barrier of the Pennine hills that separate Yorkshire from Lancashire
it seems unlikely he was driving sheep (or their shorn fleece) to Liverpool. The wool trade
was more likely to be centered on the Yorkshire town of Leeds. Liverpool, on the other hand,
was a major port for trade with the Americas and the population would already contain a
mixture of races. And where you have sailors, you find a service industry catering for their
needs including taverns and women of easy virtue. I solved the conundrum posed by
Earnshaw's adoption of Heathcliff by positing a long term relationship with a woman of
mixed race in Liverpool who gave birth to a son who was (as noted of Heathcliff) of a
dark/swarthy complexion. Perhaps on that last visit she died or was in failing health and
Earnshaw took the boy home with him. He certainly favoured him over Hindley.
The physical bond between Heathcliff and Cathy thus became incestuous and in my view
provided the underlying reason for their doomed relationship."
Mr. Tilley was, by the way, most kind and thoughtful in his responses to my questions. His answers confirmed what I had suspected, and that was that he put a great deal of study and thought into his work on this film.