Just an FYI...
Old video games (pre 1985 for the most part) used *linear* AC transformers, with a secondary AC to DC conversion board.
The technology for newer "switch mode" power supplies had just entered the IBM PC computer world around 1981 and were extremely expensive so they wern't used in the beginning.
A large copper wound iron core transformer simply takes AC power and coverts it to either the same voltage (e.g. Isolation transformer) or a lower voltage like 5, 7, 12, 14 or 30 volts were the typical outputs of these supplies. Bally Midway, Atari, etc... all used similar but not identical ones.
The huge "big blue" (or multiple smaller but still large) capacitors were simply line noise filters to give a *somewhat* more fluid non-peaking/non-dipping AC frequency.
From the main power transformers, one goes directly to the monitor, it's called the isolation transformer. The other transformer likely has a 5 volt and a 12 volt output. But these voltages are AC not DC like electronic circuits require. Therefore it went to a secondard circuit board that typically had a few capacitors (filter noise), some diodes (to rectify the power--in other words convert AC to DC), and a couple large transistors mounted to a huge heat sink (to supply cleaner power when the AC voltage fluctates even with the capacitors), plus a few resistors that get quite hot that help keep the maximum voltage set.
From this board, the power then goes to the game board for 5 VDC chip logic and 12 volt DC audio amplification.
On most games, this is how it was set up.. e.g. all Atari, and most Midway (e.g. Galaga, Tron, Tapper, etc..) However the really old Midway like Galaxian and Pac-Man/Ms.Pac actually had the power board on the main circuit board and therefore AC power went directly into the gameboard. Of course this lead to frying of the traces on the edge connector since so many amps were being sent through it to get there. Later they converted to the separate boards (which also would die, but wouldn't require working on the main game board)
Finally around 1985, the replacement "switch mode" power supply came about. In a nutshell, it's identical to an old "AT" (pre-ATX) computer power supply, minus the fan. It doesn't use large AC transformers, instead it changes the frequency of the power (increases it) and then uses little tiny transformers instead, and converts it to DC and reduces the frequency back to 60hz. Usually they are controlled by at least 1 computer chip to provide a clean stable power source.
They don't take the place of isolation transformers for monitors, but do replace the large power transformer(s) and secondary power boards.
Therefore, in many games, you can rip out the large transformer/capacitors and the secondary board, and wire in a replacement switch mode power supply. On the positive side your board will run better and longer as you're giving it a MUCH cleaner source of power. On the negative, you usually have to hack your wire harness and what not to connect it in (though not too bad in *most* games), so you're no longer "original"---if that matters to you.
Specifically regarding the Atari AR boards.. They combine an AC to DC power conversion *and* the audio amplifier in one, so if you get rid of it, you'll need to put in an audio amplifier like out of a computer speaker system.