How to concatenate all token values of a list in a single field within a Rules loop?
If what you're looking for is not available, then just make it available, which is "a different way to concatenate all of the URLs of each file" (as in your question). Read on for more details ...

Have a look at this example of a Rule (in Rules export format), which is a variation of what you're asking for:

{ "rules_show_list_of_fields" : {
    "LABEL" : "Show list of fields",
    "PLUGIN" : "reaction rule",
    "OWNER" : "rules",
    "REQUIRES" : [ "rules" ],
    "ON" : { "node_insert" : [], "node_update" : [] },
    "IF" : [
      { "node_is_of_type" : { "node" : [ "node" ], "type" : { "value" : { "article" : "article" } } } }
    ],
    "DO" : [
      { "variable_add" : {
          "USING" : { "type" : "text", "value" : "StartOfList-" },
          "PROVIDE" : { "variable_added" : { "email_list" : "List of eMail IDs" } }
        }
      },
      { "LOOP" : {
          "USING" : { "list" : [ "node:field-email-addresses" ] },
          "ITEM" : { "current_email" : "Current eMail" },
          "DO" : [
            { "data_set" : {
                "data" : [ "email-list" ],
                "value" : "[email-list:value][current-email:value]-"
              }
            }
          ]
        }
      },
      { "data_set" : { "data" : [ "email-list" ], "value" : "[email-list:value]EndOfList" } },
      { "drupal_message" : { "message" : "The value of the email_list variable is: [email-list:value]." } }
    ]
  }
}


Here is a summary of what this rule does:


Add a new variable email_list.
Init the email_list value with some prefix.
For each item within the loop, append the value of that item, followed by a separator character.
Add a suffix to the email_list value. 


In my case I'm using a multi value text field with machine name field_email_addresses, which contains eMail Ids, and just want to dispay a Status message with a concatenation of those eMail IDs, separated by a "-", and with a prefix (=StartOfList) / suffix (=EndOfList). And I also use Rules Events "Update existing node".

Replace the machine name of my list field to your list field, and replace all 'eMail' by 'file' and you should be able to import this rule in your own site (if you have the Rules UI enabled).

Not sure if you want the prefix or suffix, and/or the separator character (="-"). Adapt or remove any of these to fit your needs.

Voilà ...

Demo

Here is how the Status message looks like after you create a new node, or update an existing node (of type Article):


  The value of the email_list variable is: StartOfList-user2@example.com-user4@example.com-EndOfList.