This sentence (with the usage of indefinitely) is quite confusing

Does this mean "Realizing the fight has the ability (has the possibility) to go on indefinitely, he decided to switch up his strategy."

Yes. That's what it means.

He realized this as they were just going back and forth as they had the same technique.

Let me rewrite this sentence for clarity:

He realized this since they were just going back and forth since they had the same strategy.

Does this preserve the meaning as you intend it?

(I dislike the use of as as a synonym for since. It's confusing.)

Anyhow, whether they are using the same strategy is not stated or implied.

Does "could" mean "would" in this scenario? Why or why not?

No. There's a slight difference: Would means it will go on forever. Could means only that it's possible.

I don't really understand this as how can a fight go on forever? It's just not possible. Can someone tell me the meaning fot his sentence? Is it sarcasm?

Not sarcasm. The idea is that a fight would go on forever if the two sides were evenly matched. Thus, there would be no winner and no end to the fight.