The two things I see there are:
1) the parent ID of the computer properties table is the EPOLeafNode AutoID; so it would make more sense to select EPOLeafNode.AutoID directly
2) I think you just have to use double quotes around the computer name (double quotes worked for me but singles didn't).
https://localhost:8443/remote/core.executeQuery?target=EPOLeafNode&select=(select EPOLeafNode.AutoID EPOComputerProperties.ComputerName)&where=(where(eq EPOComputerProperties.ComputerName "COMPUTERNAME"))
That's it! Thanks.