Is it possible to extract audio digitally from a (Video) DVD?

Yes, but not using EAC and though it’s more manual work. For an unprotected DVD, the only hardware you will need is a DVD drive and a software to demultiplex the VOB files into the audio streams (usually compressed in AC3 or DTS). Then you need a programm to decompress these compressed files (a AC3 decompressor or a DTS decompressor).
“Real” Audio DVDs and SACD have a compression scheme that is not yet by software decodeable (MLP from Audio DVDs should be playable with some Creative hardware though).