Typically when there's a variant of an ARX algorithm that goes from 32-bit words to 64-bit words, we do increase the rounds. As DannyNu mentioned, BLAKE2 is a variant of ChaCha, and while BLAKE2s (the 32-bit version) uses 10 rounds, while BLAKE2b (the 64-bit version) uses 12 rounds. One round of BLAKE2 is equivalent to two rounds of ChaCha, so we'd likely want to use a 24-round variant of 64-bit ChaCha.
Similarly, SHA-256 and SHA-512 are ARX designs based around a block cipher that's retroactively named SHACAL, and SHA-512 has 80 rounds, whereas SHA-256 has 64. Keccak, which is not an ARX design but works in a somewhat similar way, also has more rounds between its 32-bit and 64-bit variants.
The typical reason we would add rounds in this case is that with more bits, we must do more work to ensure each key bit or input bit has an effect on all of the output bits in the proper way.
How many rounds should be added depends on characteristics of the cipher, like metrics on the avalanche effect and resistance to linear and differential cryptography. If we were designing an algorithm that was a 64-bit variant of ChaCha, we'd investigate these criteria and probably try to extend the best known attacks on ChaCha to our variant to see what the right additional level of rounds would be to have a similar level of security.
