Chelsea failed to capitalise on Man City's failure to beat Brighton at home on Saturday and they didn't increase the points gap between them and the City. The Arsenal was simply a better team. Although the game stats look fairly even, it's Arsenal who created much better chances.
As for Man City, they should really push hard and try to do whatever it takes to finish in the top 4 to earn a place in the next season's Champions League. They are awaiting a verdict to their legal battle with the Premier League, when they are charged with 115 instances of rules violation. They will likely end up with big financial penalties as well as possible points deduction, so participation in the Champions League could ease financial losses they might incur.
You wouldn't totally blame Chelsea for failing to capitalize on the draw that Manchester City played with Brighton to increase their point difference with Manchester City in the Premier League table because Chelsea played against a tough opponent, which they found difficult to beat. This season Manchester City is not the same Manchester City that won the Premier League title for 3 consecutive times; they are struggling to win their matches in the Premier League, so I don't see them as a threat for Chelsea in the race for the top four finish even though Chelsea is leading them by one point in the Premier League table. I see Newcastle United and Brighton as the clubs that will be a threat for Chelsea in the top four race, so Chelsea needs to keep winning their matches if they don't want either Newcastle United or Brighton to overtake them in the Premier League table.