Yes, ACI supports specifying port ranges for container groups and you can specify both UDP and TCP protocols for a given port or range in ACI.
Instead of using iptables, you'll need to rely on the port mappings provided by ACI as iptables within the container isn't supported.
Try to create a container group with the port config using the cli
az container create \
--resource-group your-resource-group \
--name your-game-server \
--image your-game-server-image \
--ports 27015 27015 27020 27000 27005 27031 27036 \
--protocol TCP UDP UDP UDP UDP UDP UDP \
--ip-address public