Chi-squared test assumption of independence

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I'm somewhat new to inferential statistics, i want to apply the Chi-squared test for independence on a football data-set, basically i am trying to see if a team that makes more shots on target is more likely to win the game.

My data-set is as follows:

╔═══════════╦═══════════╦════════════╦════════════╦════════╗
║ Home      ║ Away      ║ Home shots ║ Away shots ║ Result ║
╠═══════════╬═══════════╬════════════╬════════════╬════════╣
║ Juventus  ║ A.C.Milan ║ 9          ║ 4          ║ H      ║
║ Inter     ║ Napoli    ║ 2          ║ 7          ║ H      ║
║ Roma      ║ Lazio     ║ 5          ║ 6          ║ A      ║
║ Udinese   ║ Juventus  ║ 3          ║ 7          ║ A      ║
║ A.C.Milan ║ Roma      ║ 5          ║ 4          ║ D      ║
╚═══════════╩═══════════╩════════════╩════════════╩════════╝

In my Chi-square table i have something like

╔═══════════╦═════════════════════════╦═════════════════════════╗
║           ║ Home shots > away shots ║ Home shots < Away shots ║
╠═══════════╬═════════════════════════╬═════════════════════════╣
║ Home wins ║                     119 ║                      62 ║
║ Away wins ║                      45 ║                      64 ║
║ Draw      ║                      41 ║                      49 ║
╚═══════════╩═════════════════════════╩═════════════════════════╝

Since the same team can be computed in more than 1 cell, is this breaking the independence assumption?

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No, because though its the same team, its a different setting. Yes, its not exactly in line with the requirements of independence as you would see in theory, but we can intuit that it will be different enough for us to apply the test. I have seen a lot of problems set up like yours, and it's without a problem.