Liverpool beating Arsenal doesn't mean anything in the grand scheme of things for the short term, because lets be honest Liverpool will lose a game too, it's possible for them to go unbeaten but I doubt it, they will lose, and Arsenal can cover that difference.
That assumes Arsenal will win whenever Liverpool loses. I think last season or the season before that shows that Arsenal struggle to close the gap when it matters.
It is indeed a long league, and even the best-prepared teams can sometimes make mistakes. But Liverpool's victory at least gave them maximum points and put them in a better position to close the gap. We all know how unpredictable the EPL can be. Smaller teams can change the course of the league. They can beat the big teams and vice versa. So, the best strategy is to always get 3 points in every league game. Because the league is decided by many games and all of them are important.
I think Liverpool's victory over Arsenal is absolutely crucial. Besides getting three points, it also provides a great start to their second match. Liverpool and Arsenal will face each other again, so winning the first match would certainly be a huge advantage. Therefore, Liverpool will benefit from this. Therefore, if you say that a Liverpool victory over Arsenal isn't important, you're wrong. As Luzin said, all matches are important, and I agree with that. Winning every match in the Premier League earns points, and those points are what will lead a team to the championship.
Furthermore, if you think Arsenal can overtake Liverpool, it's possible. The Premier League is just starting, so anything can happen. However, I personally believe that even though Arsenal has performed well this season, Liverpool will perform even better. Moreover, as we know, Arsenal has consistently experienced a decline in performance as the league draws to a close for several seasons now. So, it's possible that this could happen again this season. With that in mind, I think Liverpool remain strong contenders for the title.