Hi, sorry for late reply.
The only reason I know of that would make the plugin not appear in the list is the path to jdk being wrong.

I can see you have a i386 jdk, which is not strictly speaking the same as x86. But I can understand the confusion 😀

Try here
https://adoptopenjdk.net/releases.html?variant=openjdk8&jvmVariant=hotspot

Haven't tried with wine myself but I think it should work