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. They need to win every game to make sure they can win the title. Being complacent and believing that your competitor will slip up because you did is not really good. That being said, I think this applies to every team, not necessarily Arsenal only.
The chances of Liverpool losing in the English Premier League this season are actually low because Liverpool have strengthened their team quite a bit this season, so for now, I don't think any other team in the English Premier League can beat Liverpool so easily. In one match, we saw Arsenal compete hard against Liverpool and the match went to a draw but at the last minute, a Liverpool player scored a goal to ensure the team's victory. I don't see the possibility of a tough competition with Liverpool from Manchester City. If there is a tough competition with Liverpool, then Arsenal or Chelsea will be the opponents in that match. So for gamblers around the English Premier League matches, betting on Liverpool can be relatively effective because Liverpool has a higher chance of winning in most matches.