Hi,
That is a different issue.
I was talking about the fact an Application does not have to be in the Application Folder of the computer you are using.
Basically it will set up files and the like on your current computer even if you access the Application via File Sharing.
What you are proposing is running the app on the Original computer with access to the files it has already created but seeing it on your Display (Screen Sharing).
On the computer that will be Host go to System Preferences > Sharing and turn On Screen Sharing.
You may want to set an Account Name and a Password to access this if doing it over the internet.
It will still ask you to access the computer from your current computer with an Account on the Host and it's password.
LAN based access.
Lets say the computer in question appears in the Shares section of the Finder.
You have two ways to start what can be referred to and the Finder's Screen Sharing.
1) using the item in the Shares the window will show "Connecting" and give options to Screen Share and Connect As.
I am already connected in this Pic (Standard File Sharing)

Using the Screen Sharing Button will launch this icon and bring up the Dialogue box

the default User Name will be the Account on the current computer.
You will need to change this to the account you are going to Log in on to the other computer with.
And fill in the password.
2) Finder > Go Menu > Go to Server and enter VNC:// (instead of AFP or SMB) in front of the IP address.
It is greyed out in this pic as I already have that dialogue box open

Using the Connect button will bring up the App icon in the Dock and the Dialogue box again.
Having singed on to the other computer then you will get a Window showing the Desktop (or any open app window)
Here in this Pic I have clicked the Applications Folder's icon in the Dock

The window is not the "front" one because when it is the CMD+Shift+4 works on the MacBook Pro and it is not grabbing shots on this computer.
You can do the same from a remote location.
However the IP used is then the Public IP and the routing device has to then point the request to the Host computer.
iChat and/or Messages Screen Share can get around the User Name and Password issues and the router processes.
However the iChat Auto Accept does not work in it's current form for Screen Shares.
One thing.
This Process via iChat/Messages or the Finder is like using that computer as if you were there.
If it happens that there is also a person already using it they can't continue doing what they were doing.
The iChat/Messages version does include a Audio Chat alongside so it is great for remote Help.

8:28 pm Thursday; March 6, 2014
iMac 2.5Ghz i5 2011 (Mavericks 10.9)
G4/1GhzDual MDD (Leopard 10.5.8)
MacBookPro 2Gb (Snow Leopard 10.6.8)
Mac OS X (10.6.8),
Couple of iPhones and an iPad