I have a whole tube full of high sided switches that match this but you need a FET not this device.
the input threshold voltage is 2.2 volts. Is that the amount of voltage needed to switch the gate?
No it is the voltage when the gate starts to turn on. At this point it will be operating in the linear mode and so will get very hot. You need to look at the fully saturated gate voltage. That is normally given when they quote the On resistance between source and drain.
For use directly with an arduino look for a "logic level" FET like the IRF7862PbF or the IRLI640G.