DPS is significant for this fight in a number of ways:
1) DPS needs to quickly burn down the first two adds that spawn during p1. They then need to DPS Anub as much as possible before he submerges.
2) As soon as Anub submerges and p2 begins DPS needs to quickly do 2 things. First, they need to burn the 2 adds that have been OTed through p1, and then they need to quickly kill scarabs as they spawn throughout p2.
3) DPS needs to get Anub into p3 in 1 or 2 submerge phases, otherwise it's likely a wipe due to Anub's enrage timer.
4) Lastly, if you do make it to p3 with sufficient time left on his enrage, you need to do enough DPS to outdamage his HOT/leech effect which is constantly healing him. This is noticeably less extreme in normal mode, but still a factor if DPS isn't up to par.
Everytime I PUG Anub (in either 10 or 25) wipes are a direct result of poor DPS. DPS need to not die to dumb things (as in, anything that hurts you in p2) and they need to be able to pump out high levels of efficient DPS while switching priority targets quickly.