brad nail will not close the gap and hold no matter how many nails you shoot.

Titebond wood glue and clamps.

I'm with ForceFlow but I would also add some trim head screws and zipper it before installing the decals. Apply some wood glue on the screws before setting.

Pipe clamps.

Do you have the inside corner brackets?

I would. You want to clean up the joint, apply titebond 3 and clamp and screw. Afterwards reinstall the corner block.

There is only one way to fix it.

None of your quick and dirty fixes will hold. Pinball machines are heavy and need heavy repairs

check all corners for looseness and address them.

Remove the wood block and make a new one. You can cut a corner off a 2x4 with a skill saw to make blocks.

Buy 4 3/4" pairs of pony clamps (harbor freight, 2 packs) (8 pieces) buy 3/4" black pipe cut at home depot, each piece threaded on one end.

2 pieces for the length, 2 pieces for the width. cut them 1' or more longer than the cabinet, both ways.

Spread out the corner, scrape out any loose wood fibers and flood it with titebond 3 glue. Use pony clamps and pipe as a spreader.

Reverse the pony clamps ends and clamp the corner.
While at home depot get 8 or 10 hardwood floor sample squares to use under the clamps to keep from denting the cabinet too much (they are free). I like the maple composite ones

You want 100% squeeze out of the glue all along the joint.

wipe off all the excess glue with a wet rag.

Put plastic or wax paper under the clamps to keep from gluing them on.

Get a ryobi brad nailer if you dont have one. get 2" and 1 1/2" brads also some 1" ones for other things.

Using 2" brads Nail the corner from front and side with 4 brads each side starting 1" from the top and 1 1/2" from the bottom.

Wait for it to dry. Glue in a new wood block with titebond 3, clamp it on or wedge pipe against it. Using 1 1/2" brads nail it 8 times.

Clamp a leg on the cabinet to use as a drill guide to make new holes for the leg bolts

sand out the cab, fill it and primer it.

Make sure there are no bumps, everything shows under the decals

Easy enough.

Pinballinreno said it pretty well but should you need further info, vids guide to cab restoration might help

https://pinside.com/pinball/forum/topic/cabinet-restoration-vids-guide

I'd also upgrade to the "beefier" leg brackets:

https://www.pinballlife.com/desegastern-leg-bracket.html

Here's the bally/williams style: https://www.pinballlife.com/williamsbally-new-style-leg-bracket.html

I use the heavy duty wider ratchet strap around the whole cabinet to close the gap after filling with TitebondIII. Then install the new triangle wood also with TBIII and screws. Install the deluxe leg brackets. Let it dry. Remove strap. Done.

Its really the only way.

Bondo, half-time, glazing putty and primer.