74LS189 chip overheat
Per your circuit description chip should not heat - there's no over-current drain, and no electrical conflicts at its outputs.

If you search over internet using query "74LS189AN heating", there's a video by Ben Eater exactly on the subject, with people comments (expand the replies on that page to see them):


  Please, help me! When I put 3rd (WE) pin of 74LS189AN to the 5V, chip starts to heat up. Whats the problem?


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  Hi! I also have this same problem and have ordered from two different ebay sellers already and they are all faulty. I cheched Jameco but they do not ship to Finland. Anyone here have any other site where these can be ordered to Finland?


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  Same thing here. ordered replacements from jameco electronics in the US, they work fine. thanks!


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  I too decided to order more expensive 189's in the end from a UK seller (the batch that didn't work were a cheap Chinse import ... I know, I know). The replacement parts worked exactly as per the datasheet.


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Here's comment from Ben's page you refer to in your question:


  To whom it may concern,
  I purchased the 74LS189 chips from the Ebay link Ben provided. Specifically, I purchased them from a supplier called “j_k parts”. The chips did not work and heated up very quickly, I followed the RAM videos multiple times and consulted the datasheet to ensure I wired the chip correctly.
  
  I found this article on Reddit today (http://www.righto.com/2017/08/inside-fake-ram-chip-i-found-something.html) about relabelled (counterfeit) TTL chips and the author specifically examines the 74LS189.


So question to you - where did you source yours?