What is the explanation for the strange spelling of the English word playwright?

This is not a strange spelling. It is analogous to 'shipwright', 'wainwright', and 'wheelwright', for example. It means a maker or repairer, and ultimately derives from the same Old English root as 'work'. Compare 'wrought iron' ('wrought' being an old form of the past tense and past participle of 'work'). Compare 'overwrought'. Compare 'What God hath wrought'. These are all related forms.