Thirding agreement on rebuilding, and it doesn't look like you need many things at all. Third agreement also on a clutch, your grandson doesn't need the additional danger of higher speed from a "torque converter" (CVT, aka Constant Variable Transmission).
The Harbor Freight engine is called a Predator 212cc, 6.5 hp., 4-stroke, overhead valve, air cooled, pullstart engine. There's many opinions on which of the 2 versions are best or make no difference, the hemi or non-hemi. These are easily identified by their valve covers with OHV on them, the shiny, flat, octagonal, stamped out non-hemi, or the duller, rectangular, domed on top cast aluminum hemi. Easier by the H.F. part # which I forget. Caution: If you have a preference, don't go by the picture on the box. Punch out the handhold on the side, reach in, and feel the valve cover. My hemis come in a box with a picture of a non-hemi on it. All agree that aftermarket parts do make a difference, hemi or not often must be specified.
They sell for $129.95 every day, but regularly go on sale for $99.95 with a tear-out coupon from a flier, or maybe coupon not needed. Warranty is only 30 or maybe 90 days, an extended warranty is $50.00 for a year. I did that knowing it would be way past OEM warranty before finishing kart and running motor. Wasted my money. Didn't think about it being basically impossible to get motor back to OEM condition for returning it if needed after modifying it to about 15+ hp., but might be a good idea for you.
Add a chain, looks like the standard #35 chain, a #35 master link to clip it together with, attach that throttle cable to it, set tire pressures, and it should be ready to go. See youtube for many how-to videos for hooking up a throttle, type '212 throttle' in the search bar. Speaking of...........
That throttle cable and the brake rod are both just laying there on the floor looking like your heels will be resting on both when driving. Really need to fix that, could be a serious safety issue.
--edit--
OOPS! Sorry about that, forgot to talk about your mounting and sprocket issue. Your motor mounting plate won't accept a Predator, the back of the seat is in the way, your motor would have to go further back, must cut out the plate, move it, and reweld it, or get another plate to weld in.
You also need to get another sprocket, install it on the axle on the LEFT side of the motor, or move your existing one over to the LEFT side of the motor. This is true of any engine with CCW rotation of shaft (looking at end of shaft).
I recommend mounting the motor with its output shaft as far back away from the axle sprocket as possible to get more chain teeth wrapped around and in contact with the small (likely 12-tooth) sprocket on your clutch. Don't forget your chain lube.