I got everything to work fine and the game runs properly.
The only issue is the contrast of the LCD. The text and my character blend in with the background squares making it hard to see. I have checked the V0 and everything seems to be fine!
I have attached the code as text and Arduino file.
Looking closer, it appears you don't have the I2C version of the LCD, and so likely there is no built-in potentiometer, but you could attach one to it if you want.
OK, put a 1k potentiometer or actually, "trimpot", wired as a variable resistor which is to say the wiper connects to one end, between Vo - pin 3 - and ground.
Do not connect the potentiometer to Vcc - you may see this done but it is in fact wrong.
If you do not have a trimpot (10k would do, but 1k is better), just try a 470 Ohm resistor between Vo and ground. Also try 330 Ohm or other values up to about 1k.