Wow soo much confusion of terms here.
Think of the internet like a water moving through something.
Speed in Kbps, Mbps, or even Gbps is the actual flow rate of the water.
Bandwidth is the amount that can flow through the river at any given point, which is basically how wide and deep the river is.
Latency is if there are any small damns or gates the water has to wait on.
Caps are if there is a dammed up lake at the end that prevents any more water from flowing except at a trickle after the dam.
So water can move just as fast through a garden hose as it does a river. However, the river is going to have far more "bandwidth" that allows for more data at a time to move compared to a garden hose.
So in reference to the OP's question, most games don't use that much bandwidth. However, the bandwidth usually provided by a cell connection is not usually much. Data that flows through that isn't using the full bandwidth my move quick enough, like loading a web page, but playing most games is going to be more bandwidth than most cellular connections will allow. Which if you start needing more bandwidth than provided you'll get slower on your data transfer, which will up your ping and slow down your transfer rate.