The 7805 looks to be a +5V regulator (i.e. a VRM). These tend to get extremely hot, especially in such limited form factor (size). The reason it's screwed down is to help dissipate heat through the aluminium/metal heat sink. Example photo (ignore the capacitor, it's unrelated to the question):
https://console5.com/techwiki/images/th ... Output.jpgThus: is the screw important? I would err on the side of caution and say yes. Different SNES revisions/models have this done differently. If the VRM is also soldered or attached to the heat sink directly, then it might be OK (but the more heat dissipation/transfer the better!). If it's one where it's only in contact to the heat sink using the screw, then yes, I would say it's incredibly important.