Config: Prevent pad settings lingering in game properties blocking profiles

[RedPanda4552]

Description of Changes

Removes a leftover check against the old "use per-game controls" setting which can be lingering in game properties files, allowing profiles to actually load without interference.

Rationale behind Changes

Partially fixes #11764. Will allow profiles to load properly for anyone who hasn't cleared lingering pad settings out of their game properties.

Suggested Testing Steps

Create a profile with bindings very different from shared, switch profiles and verify controls still switch as intended.