I am not a native speaker, but it is absolutely clear that in your case meeting is a gerund, as it governs a direct object and it has no article.
Running in your case should in my opinion be used as "running" (quotation marks) , being just an indefinite idea of a grammatical object used like a proper noun. It's merely a name for a certain noun. But it is only an indefinite part of speech in this form.
Although English style books consider this verb use as a cliche being not recommended, I would turn better to the noun style and re-write it as a whole: It stands in connection to the running. In this form, the word running is a noun with all its functions implied. It may be used in general and/or actual, real sense (materialized) and have the plural formant -s at the end.
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