If we use the biological explanation, a living thing is defined by one that has biological processes, caused by chemical reactions.

A game is constructed of programmed processes, caused by computational algorithms.

By definition, something that is alive needs to feature:

Interaction between organisms

This is when an organism has some sort of effect on another, same species or otherwise. The passive influence of a particular game drives us to interact with other games differently, whether we be playing, programming, or talking about them. Also, as long as a game continues to influence other games around it, and it (or its "cells") are influenced by the games around it, it is communicating.

Digestion / Energy Consumption

While rather easily defined for living organisms, for vague objects such as games, this can be rather openly interpreted. This could mean anything from the game's absorption of funds, player's time, electricity usage on the systems that sustain the game, development effort, the list goes on.

Response to Stimulus

This is another easily satisfied criteria. As long as the state of the game reacts to outside events (which it does as its cells are heavily influenced by the outside world) or even internally (caused by mechanical alterations of the game itself) the events that unfold inside the game change dynamically and intelligently in reaction to that.

Cell Growth

As an organism progresses through its life, its cells grow, die, and are born anew. The same could not be more true for RPG games and their players. New cells a born whenever a new player enters the mix. This can be induced by something as straightforward as official advertising or by something as subtle as word of mouth, forums, results on Google searches, etc.

Reproduction

This is not a mandatory trait for something to be classified as alive, although it is required for a species's continued existence. Games, like creatures such as mules, are generally "sterile" unless artificial reproduction is involved via outside interference (such as ports, relaunches, and copy+pasting mechanics into sequels)

There are a couple other things that can be used to determine if a biological organism is alive, but I think I've said enough.

So what do you think constitutes the life or death status of a game?