sflorlando, IF the 2 flat blades on the plug you bought, will fit into the socket in the wall, you are good to go. The dryer socket should be 30A and if that plug is also 30A you can use it. They might be spaced too wide to fit.
The wires in the cord are not typical USA code. All you need to do is, open up the case on the welder, and see which wire (green hopefully) is attached to the case somewhere. The other 2 wires will be the 240V connection wires to the coils in the welder.
Open up the plug you bought, and it is very simple to wire up. CAREFULLY measure each wire, so you cut them at the correct length, so there is no bare wire showing outside the clamps on the blades, AND, so you do not have extra wire to stuff inside the plug housing. After measuring, remove each blade and attach the correct wire to the correct blade, and close up the plug. There should be an external clamp with that plug, that grips the entire cable with the black covering, so you don't jerk the wires out of the plug.
The round-split blade will be ground. That is the wire that you find connected to the welder case. The 2 other wires are the 240V LEADS. It DOES NOT matter which of the 2 flat blades
you connect those 2 wires. The round (NOT split) blade may or may not fit in your socket . Just leave it out of the plug housing.
If you get lost, just post again.