The code is good regarding the inputs. I hope You noted the change needed for the button connections, between the input pin and GND....
The debounce time of 500 mS will surely cover the bumps in the switch! I suppose You don't score 100 000 within that time...
I havent't analyzed the rest of the code much.
As already suggested You can simplify the code. In setup, and in New game, You inactivate all the 100 000 indicators, digitalWrite(pinX, LOW);.
Then:
if (k > 0 ) digitalWrite(LEDpin1K, HIGH);
if (k > 1 ) digitalWrite(LEDpin2K, HIGH);
if (k > 2 ) digitalWrite(LEDpin3K, HIGH);
if (k > 3 ) digitalWrite(LEDpin4K, HIGH);
if (k > 4 ) digitalWrite(LEDpin5K, HIGH);
if (k > 5 ) digitalWrite(LEDpin6K, HIGH);
if (k > 6 ) digitalWrite(LEDpin7K, HIGH);
if (k > 7 ) digitalWrite(LEDpin8K, HIGH);
if (k > 8 ) digitalWrite(LEDpin9K, HIGH);
If You like the idea...