Skipping wifi is correct to set up android-x86 in a virtualbox.
I don't know why you got problems.
From your screenshot the Ethernet has got IP correctly.
I see no reason why it can't work.
The only explanation is your virtualbox was blocked
by your network environment (firewall, proxy, ...)
You should check that.
There are already some videos on the Youtube that teach you
how to use android-x86 on virtualbox. Just take a look, say
As shown in the video, the internet works fine.
No any special configuration is needed.