You still use paper. Instead of writing the game in a general purpose programming language you write it using logic gates. You get abstraction and modularity by designing larger components (adders, flip-flops, timers, shift registers) on separate pieces of paper and then including them as named black boxes in a higher-level diagram.

The good news for the Pong developers is that most of those larger components were already available off-the-shelf. Common families of these chips, such as the venerable 4000-series and 7400-series logic families, began to appear on the market in the mid-1960's.

Edit just to add another bit of nuance. If it still seems like an extremely difficult task without much precedent, I think the lineage of these early arcade games can be traced back through their older arcade siblings: pinball machines. People had been building more and more sophisticated pinball machines over the decades since their inception in the early 1930s. For a look into pinball machines, some of their history, and an amazingly deep dive into the workings of a 1970's model, check out Alec's pinball series on Technology Connections [1].

[1] https://www.youtube.com/watch?v=ue-1JoJQaEg&list=PLv0jwu7G_D...

Wouldn't it be closer to say that the game was the computer?

A very simplistic and non-general purpose computer, but a computer nonetheless?

Bit heavy on the academic theory, but Claude Shannon's "Mathematical Theory of Communications" might help with the link between gated logic and modern computation.

CS builds/extends hardware based on Shannon's work. CS programming languages are classified according to the Cholmsky hierarch in theory of computation. Given topic of discussion, atari games implimented as logic gates are a form of state machine (autonoma) which can be represented at a higher level of abstraction by a programming language. ( https://www.geeksforgeeks.org/chomsky-hierarchy-in-theory-of...)

There are different frameworks / ways of implimenting/presenting 'logical computations'. aka ME physical, EE logic gates, math numerical computation, computer science programming languages.

Loosely ordered by various implied collision/response (XOR) for anaylzing/presenting "logic/type groupings" in physical spaces / virtual spaces.

Higher level/virtual logic/techniques of modern CS hids the 'logic bits' of things. aka gawk chapter "11.3.11 And Now for Something Completely Different" program -- where character fonts are higher order of logical groupings tied to a number of bits ( https://www.gnu.org/software/gawk/manual/gawk.pdf ) and pdf imaging ( https://github.com/tavinus/pdfScale )

Historical progression of display mechanics has less virtual abstraction relative to how programming languages produce/compute results.

No player movement, all autonoma state machine : https://www.youtube.com/watch?v=wiYTxjJjfxs

Progressing from "larger" implimentation to smaller implimentation details for equivalent amount of "logic states":

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A) mechanical logic devices and circuits : https://www.nacomm09.ammindia.org/NaCoMM-2009/nacomm09_final...

   zoetropes            : https://letstalkscience.ca/educational-resources/interactives/zoetrope

   kinomatic display    :

   babbage engine       : https://www.computerhistory.org/collections/catalog/X39.81  /  https://www.computerhistory.org/babbage/

   mechanical pixel art : https://www.youtube.com/watch?v=w1ks0Vy98KI

   mechanical clock     : https://www.youtube.com/playlist?list=PLiqrEMrfoE8pOmxFXpOTk7UyUK8hfkwLH

   water display        : https://www.youtube.com/watch?v=L0i-uTa4kv4

  

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B) electrical logic devices (smaller scale than mechanical devices, so no vaccum tubes / flip displays):

   light gun     : https://www.reddit.com/r/explainlikeimfive/comments/5crto3/eli5_how_does_an_arcade_shooting_machine_works/

   mechanical tv : https://en.wikipedia.org/wiki/Mechanical_television

   crt ram       : https://www.radiomuseum.org/forum/williams_kilburn_williams_kilburn_ram.html

   e-ink         : https://www.visionect.com/blog/electronic-paper-explained-what-is-it-and-how-does-it-work/

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C) virual stuff:

   pixel to spreadsheet : https://leondrolio.com/apps/pixel-spreadsheet/

   mindcraft computer   : https://minecraft.fandom.com/wiki/Tutorials/Redstone_computers  
                       
                          https://www.reddit.com/r/programming/comments/xecijm/someone_made_minecraft_in_minecraft_with_a/

   bash & postscript make it a lot easier to change the display mechanics : https://github.com/tavinus/pdfScale

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