The only reason they could do this was because of
a few carefully-crafted ciphertexts, and when these are decrypted by the target computer, they trigger the occurrence of specially-structured values inside the decryption software. These special values cause observable fluctuations in the electromagnetic field surrounding the laptop, in a way that depends on the pattern of key bits (specifically, the key-bits window in the exponentiation routine). The secret key can be deduced from these fluctuations, through signal processing and cryptanalysis.
So in order to exploit this, someone must be decrypting those specific ciphertexts, so it must be a targeted attack. Also, Bitcoin doesn't do encryption and decryption so this attack would not work with Bitcoin private keys.