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(+4)

Found this post while I was looking for help yesterday, thought I'd come back in case anyone else comes across it.

I had this problem too. I've got an up-to-date standard self-hosted WP and if my iframe src was 'itch.io' then the contents of the iframe would disappear, I'd just get a border/empty box kind of effect.

A colleague suggested I looked at plugins, and I used the popular 'advanced iframe' from one - and that works great! 
How To Embed WordPress iFrame, with & without plugins
I just pasted in the code from the itch.io widget generator, and dumped it straight into a post in my WP blog, and it works. I've not tried playing the game 'in the widget' - I'm happy having the user see the widget banner and click to go through to my page on itch.io itself.