If you look further down the article you posted there is another bit that says 'parliament will implement the result of the vote'. Which was printed on the leaflet sent to every household in UK.
We do not have a law in UK ( yet ) saying referendum results are legally binding, but many countries do including RofI - and the EU managed to overturn a couple of theirs, its what they do.. too much at stake for them and they need the money.
What you are arguing though means that if remain had won there would still have been a basis for legal challenge of result and calls for another one
https://ukconstitutionallaw.org/2016...it-referendum/