In running such a game, a/the computer may freeze

Question

Having the following sentences and lines of reasoning:

Video Games are becoming more and more hardware demanding. In running such a game, the computer may freeze. (*)

My line of reasoning: the definite article is used because we want to focus on the computer that is running a game, we can process the sentence as follows: In (the procces of) running such a game (by a computer), the computer may freeze. "In running such a game" introduces a computer in the background, and in the next part of the sentence we are referring to this computer.

Video Games are becoming more and more hardware demanding. In running such a game, a computer may freeze.

My line of reasoning: the indefinite article is used because we want to focus on the fact that any computer (with poor hardware) may freeze when running a hardware demanding game.

Video Games are becoming more and more hardware demanding. A computer, in running such a game, may freeze.

My line of reasoning: the same as in the second.

I have the following questions:

1. Are all the sentences correct?
2. Are the lines of reasoning correct?
3. Do all the sentences roughly communicate the same information? And if so:
4. Which one will be chosen by a native?

I know that the legitimacy of some of the questions depends on the legitimacy of others, but I hope you will understand my doubts from the questions.

(*) I assume that no explicit referent of the computer appeared before the sentence and the word appeared the first time in this sentence.

Answer 1

All of the sentences are reasonable. In trying to choose between them, I realized that I would want the larger context. If these two sentences are part of a larger piece of writing that larger piece of writing would tell me which aspects to emphasize or focus on. Your analysis looks correct as well.

Answer 2

We don't generally do proofreading here, but you've done a good job framing your question, and I think it's worth pointing out the following:

• Video games is not a proper noun. Lose the upper-case 'G'.
• The prepositional phrase "in running such a game" doesn't sound idiomatic. I think "when running" would work better than "in running".
• I think the two sentences would sound better together if you stuck with the plural, instead of switching to the singular.

Put all three suggestions together, and we get:

Video games are becoming more and more hardware demanding. When running such games, the computer may freeze.

Getting back to your initial question, I think the definite article works fine. It's obvious from the context that "the computer" refers to "the computer that happens to be running the game".