Not needed as long as the tank level is 3" over the carb, and the carb is a gravity feed type.
If the Tri-Z came with an over over carb tank and no pump, you are good.
If they came with a pump, you had better use the supplied pump.
If the Tri-Z came with an over over carb tank and no pump, and you want to run with a low tank, the rectangular pump is probably your best option, although I'd guess the tractor pump will probably work too. The pump you pictured is for dual carbs, but can be plumbed together for more flow. Most engines under 50hp would not use more than 14 lph.
The issues are flow and pressure. The smallest flow is 14 lph which is plenty. Most of these pumps are designed for gravity feed carbs and run at 1-2psi. The odd pump application out there may have a 7psi pressure which will overpower the inlet needle valve. I suppose you could check it yourself.