Palestine has a parliamentary government. Their elections use a close relative to proportional representation.
Approval voting is for executive positions. President, Governor, Mayor. Not assemblies like councils and parliaments.
Approval voting prevents the "spoiler effect". It does not enable it. Nor is it applicable to parliamentary elections, such as the example you gave.
Lastly, your comment is just weird. Equating Hamas to a spoiler. Despite the electioneering by the PLA. The subsequent extra-legal attempt to invalidate the election results that brought Hamas to power.
I'm far from an expert on Palestinian politics, but if there's a lesson to be drawn from Hamas and The Gaza Strip, it's that Palestinian politics are messy.