What would it take for the vote to be binding? The Prime Minister’s assent for a binding vote?
It would have to be a proper Act of Parliament, that went through all the correct procedures (full debate and multiple readings) in both Houses and the received the Royal Assent (which would be automatic if it had followed the other procedures). This doesn't even come close.
It's what is referred to in the British system as a Backbench Business Debate which are designed to allow 'backbench' MPs (ie, non Ministers or Shadow Minister) the occasional opportunity to raise an issue they regard as important. Seniors members of the government and opposition, by definition, do not involve themselves in these matters - they have other opportunities to outline their policies.
In essence, Labor (currently in opposition) supports the idea of the recognition of Palestine and this was a way for them to put that on record. The government (the Conservatives, Liberal Democrats, and assorted smaller groups) generally does not - and most didn't even bother to turn up for the debate on that basis which is a reason the No vote was so low.
The Yes vote was 274 - if it had reached over 300, then Labor would have been able to try and use it to put pressure on the government for a full debate - there's no formal rules on that but as the House of Commons has 649 voting members (650 total, but the Speaker only votes in the event of a tie), by convention, an issue that attracted 300 votes in such a motion is one a government could be pressured to settle one way or the other. It didn't, so it really does nothing.