I think you are using the bureaucracy plugin (?) I don't have much experience with it but have some idea about how it works. You might be able to get what you want using the snippets plugin. For instance, you could create a snippet with the following text:
[[fr:admin:form?@Name of the game@=#NS#|New review]]
You could then insert the snippet on the page and
#NS# would resolve to the namespace of the page sending the info, which is the page on which the link appears.
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Edit:
The above requires a namespace snippet:
https://www.dokuwiki.org/plugin:snippets#namespace_templates_as_snippets