lol, i meant a long read for everyone else and i'm too lazy to type all the stuff up.
to put it simply, DOA has brought a couple of things to fighting games
1. Multi-tiered Stages - this alone automatically makes it play differently to other fighting games because it can potentially become opportunities for high levels of damage.
2. Interactive Levels - in every other fighting game, the surroundings usually dont mean anything save for the walls. in DOA, the ground for example is never flat which means you will move at different speeds and your combos are different. and the fact that characters can move around the stage like the Kasumi thing mentioned earlier adds something new as well. not to mention that DOA is the only fighting game to have a good wall system.
3. Counters - in most fighting games, counters are there, but are never particularly rewarding or in fact are not even worth using. in DOA of course, its the total opposite. Counters are such an intergeal part of the game that at high levels people constantly create strategies around counters. the fact that every character has available counters just makes it even more important.
4. The Throw System - DOA is the only game were you cant break most of the good throws. this might seem like something small, but considering how powerful certain throws can be... well, i cant say much about this without showing you during gameplay.
there are certain other 'subtle' things like how stuns work and how the combo system work that make a massive impact at high levels but arent worth mentioning at casual play. a lot of the things dont really matter unless you play a lot of fighting games at high levels.
online play was a pretty massive innovation seeing as DOAU was really the only fighting game that worked well on Live.