For the time being, it only applies to elliptic curves. However, the curves in actual use are over fields of large characteristic, so this result does not break them.
Obviously, any advance in understanding the discrete logarithm problem may be a step forward in breaking elliptic curves, but as far as I know, this is not a reason to change anything for the time being - at least for non-cryptographers.
> it is likely to have repercussions especially on the cryptographic applications of smart cards, RFID chips (2), etc.
It will be easier to bruteforce RSA/DSA?