so what provides the change in kinetic energy of the system?
In standard EM theory, there are no magnetic poles, only electric ones. Magnetic force on charged particle is always perpendicular to the velocity of the particle, and thus magnetic forces do not work. Generally, if any work is done on the matter, it has to be due to other forces, either mechanical force (like normal or friction force) or electrical force due to electric field.
In your case, since there are no external forces other than magnetic, the working forces have to be internal, i.e. due to the wire itself.
There is no problem with internal forces doing net work - this happens daily. For example, consider how person on a bicycle acquires kinetic energy - the force working on the bike is due to biker and the force working on the biker is due to bike while net positive work is done on the system. The energy for this comes from the energy stored in the biker.
In the case of wire, imagine that wire consists of charged particles (conduction charges) moving inside and along a perfectly reflecting tube (the wire without the conduction charges). Magnetic field acts on the particles and would curve their motion as it happens in vacuum, if the tube did not prevent that. If the wire is held static (by external mechanical force), part of the normal force of the tube cancels the magnetic force and the rest curves the motion of the charges so that they can move along the tube.
When the external mechanical force is removed and the wire is allowed to move, the reaction forces of the charged particles on the tube can do work on the tube. The tube also does work on the charges, while net result is that net work is done on the system.
In this view the work is due to contact mechanical forces, but sometimes it is believed that all mechanical contact forces are ultimately electromagnetic forces on the microscopic level. So if we went deeper into this, the working forces are actually microscopic electric forces - the electric force of the charge works on the lattice and the electric force of the lattice works on the charge.
If the circuit is made of perfect conductor without any source of voltage, the kinetic energy increases at the expense of the magnetic energy in the space around the wire.
If the circuit is made of Ohmic wire and has a source of voltage, kinetic and internal energy of the wire increases also due to energy supplied by the source of voltage.