Yeah! Found out what the problem is.
Good news: it's not a problem with Deki Wiki.

So, you can easily resolve it without needing new bits.
Here is the problem: when you connect to Deki Wiki, PHP inherits the hostname and uses it to contact the API. This works wonderfully when the hostname is resolvable by both the browser and the VM. However, that's generally not the case in NAT scenarios.
So, how can you fix this? Easy. Open 'LocalSettings.php' and add the following line:
Code:
$wgDreamServer = "http://localhost";
Alternatively, if you're using hostnames (e.g. 'http://mywiki') to reach your wiki site, you can also add this hostname to your VM so that it will resolve it correctly when it sees it, but you'll need to do so for each wiki hostname.
Let me know if this resolved the issue for you as well.