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VNC Viewer for Android?
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Popularity Score: 3
This app was mentioned in 3 comments, with an average of 4.00 upvotes
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Your link suggests VNC, which is probably the easiest way to do it. That's not a virtual machine, it's a remote desktop client/server.
I used this tutorial to set up the server on my Pi. I haven't used a phone client in a long time but I used to use VNC Viewer. Setting up the client isn't usually much harder than entering the Pi's IP address and password.
I've been using androidVNC (different name on Play Store), it's simple and nice.
It has multiple input options so it can probably do what you want. Try all the available options, as with one of them selected, I was able to drag a folder by holding the item as far as I remember. Hope it does the job :)
Something like VNC is probably your best bet. Just remote into your home machine.