Use an SVG instead (which is even responsive). Here is an example:
<figure id='backing'>
<svg version="1.1" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 1280 504" preserveAspectRatio="xMinYMin meet">
<image width="1280" height="504" xlink:href="https://cdn.pixabay.com/photo/2018/01/24/18/05/background-3104413_1280.jpg">
</image>
<a on="tap:AMP.navigateTo(url='game1.html')">
<circle cx="243" cy="133" r="79" fill="#fff" opacity="0.15" /></a>
<a on="tap:AMP.navigateTo(url='game2.html')">
<rect x="870" y="147" width="680" height="33" fill="#fff" opacity="0.25" /></a>
<a on="tap:AMP.navigateTo(url='game3.html')">
<circle cx="889" cy="379" r="80" fill="#fff" opacity="0.1" /></a>
<a on="tap:AMP.navigateTo(url='game4.html')">
<circle cx="770" cy="671" r="73" fill="#fff" opacity="0.2" /></a>
<a on="tap:AMP.navigateTo(url='game5.html')">
<polygon id="test" points="163,587 214,492 267,473 335,483 377,603 327,631 249,658 211,641" fill="#fff" opacity="0.3" /></a>
</svg>
</figure>
The trick is: AMP actions work inside SVG's so you can add click handler that navigate to a different page or update AMP State.
Note: the SVG example is from this answer.