Considering time and effort. Even if you intend to resell the cabinet, it's value will be higher if it has a working monitor. In that case, you can sell it as a working cabinet. In the other case, it's one that needs repair.
Considering the games, you mention Ms Pacman, Donkey Kong and Galaga. I could be wrong, but I think all those were originally "vertical games". This means that the picture tube was rotated so that the longest end went from top to bottom. Your Global Arcade Classics is basically using a vga style monitor and a pc as driving motor. This is pretty much also what you will find in most Mame cabinets. The only difference might be in the interface board that connects the buttons and joystick contacts. It has an usb connection to the PC. I have no idea what software the Global Arcade Classics is running. (It might be a linux derivate with Mame on top of it.), but it shouldn't be that hard to make a Mame system out of it, with all the games you desire. (Obvious racing games don't make much sense if you need to control them with a Joystick.) It will take some of your time to get things right, but it shouldn't impact much on your budget. You could start with simply a harddisk so that you can leave the original intact. The advantage of this is that you can fast revert to it's original state, if you like to play a game instead of messing with the system. Maybe your time is way to valueble, and you just want a quick way to play some older arcade games. This is not something I have an answer 4. Note that mame is capable of emulating vertical games, but you loose some of the picture tube surface on those. Those who trully want the original look and feel use different cabinets for vertical and horizontal games.
No matter what you decide to do, don't trash the monitor. 4:3 CRT monitors become a rarity on the market, as it's all 9:5 or 10:5 and LCD nowadays. I am sure someone will be willing to take it over from you. Only issue is their weight. You need someone from the neiborhood that can come pick it up. Shipping isn't recommended.