PowerApps are not as fancy as iPhone Appa, but what I normally do is to fake my way around this. For example, I would:
- make a screen shot of the island
- save it as a file
- add it as a simple image (images are square, but you can round of edges with the 'border radius' property
- if you want to have nice buttons on your island (like the pick-up/decline buttons on your sceen shot) you can repeat the procedure of pasting images. An image also has an OnSelect property, so it can act once it has been clicked.
- if you want to add some animation, you can add a timer, and make the X or Y property of your image(s) dependent of your timer value.
- you can hide or show your island after an amount of time with a combination of changing a variable in the OnTimerEnd of your Timer and using that variable in the visible part of your image.
Would that be enough for you to get started?
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