The Literal Commandment
"If the place which the LORD your God chooses to put His name is too far from you, then you may slaughter of your herd and flock which the LORD has given you, as I have commanded you; and you may eat within your gates whatever you desire." (Deuteronomy 12:21)
This commandment permits us to "slaughter of your herd and flock" on one condition: "if the place which the LORD your G-d chooses to put His name [i.e. the Temple in Jerusalem] is too far from you. If that condition is not true then the place where animals should be slaughtered is the Temple and the normal process of ritually slaughtering the animal would be followed. The permission given in this commandment is only on the location... not the process.