Pre-populate an Entity Reference when Adding a Node : Based on URL Alias
Your latest update mentions you're having trouble constructing the link, so I'll focus on answering that. 

It seems that if you construct the link manually (simply type in the addressbar) everything is working correctly (this is to test that the Entityreference prepopulate module is working correctly on your side). 

The problem then seems to be how to construct the link automatically for each of your game nodes, so that by clicking on the link, a Profile creation form is shown with the relevant entity reference prepopulated. 

Add Prepopulate links to Views


In your Games views add a field Content: Nid and Exclude from display
After that field (it's important the Nid comes before this) add a new field Global: Custom text
In the Text textarea of that field enter:
&lt;a href="/node/add/game-profile?field_gmeprfl_game_eref=[nid]"&gt;Add new Profile referencing this Game&lt;/a&gt;  

Check that the token really is [nid] under Replacement patterns. 


Now you have a list of Games with links that when clicked open the Create profile page with the related Game pre-selected. 

Add Prepopulate links to Node pages

If you need to display the link on the actual node page, you can se the same Views as above only create a Block with a Contextual filter. 

This has to be done through Views block because the module you're using (Entityreference Prepopulate) doesn't have the URL widget feature implemented so you have to work around it. 


Create a Block display View of Games
Add the same Fields as above (use the same Views)—the hidden Nid and Custom text with the link code. 
Add a Contextual filter Content: Nid and configure it:
When the filter value is NOT available
Provide default value
Content ID from URL   

This will limit the list to show the Prepopulate link for the current node only, otherwise it would show links for all games, like above.  

This filter isn't responsible to the link contruction! Link is being constructed using the Fields!
Place your block in Content region or whereever you want the link to display, restrict the Block visibility to Game pages


Visit some Game pages and click on the links, see they are prepopulated with the nodes where you clicked the link.