>> Can anyone point me to a replacement part?
Nope. Neither Mouser, digikey or any of the large distributors stock (long since retired) end-of-life components like the 2114. There are no modern equivalents as applications don't have use for such low density memory (its only 1K x 4 bits in a large DIP package).
Some other general electronic component dealers who have them are jameco, futurlec (though their shipping is very slow) and unicorn. And obviously lots of folks who specialize in arcade stuff have them.