There should be some similarity between your code and the one
@Dagobert posted even doe they are not the same. you can simply copy part of a code and replace in your code. look at the code he posted again and compare it with yours, i have red mapped the important part you should look out for.
The code above is what most html developers will use to control playlist they create, with your case you should look for the code ( shuffle':false,) and change it to ( 'shuffle':true,) or maybe the command shuffle is not in you code, in that case you have to add the code manually.......
To add the code, just search for the code 'autoplay':true,, and add 'shuffle':true, after it....
it should look like 'autoplay':true, 'shuffle':true,
Now true means yes, and false means No ( so you can even decide to set 'autoplay':false,) in that case your playlist will start automatically........ you can play around with the commands to suite your needs
Try it get back to us here......