I don't ever feel sore though. I'm afraid that I'm not seeing the gains and muscle definition I want too because of these training style. I should have abs, but don't see them. And before anyone says diet, I'm a vegan who eats whole foods and barely ever anything processed. Any advice?
To gain muscle you need progressive overload. By the looks of it you train very intense, but in a different way.
If you want to gain muscle, you should train a bit less, I'd say 4 to 5 days a week, and go heavier on your lifts. You should try a 5x5 program on your compound lifts, this is highly effective. Resting periods and a proper diet are as important if not more than the lifting itself, keep this in mind.
You say you're vegan, which is great! But you need to make sure you are getting enough nutrients to gain muscle, if you're eating 2000 calories a day but also burn that much, your body doesn't have anything to build muscle from. I would suggest a lot of lentils, beans, chickpeas, broccoli, that kind of foods.
Also, abs are made in the kitchen, as stated before. As for building the actual muscle, my opinion is that heavy compound lifts like squats or deadlifts are more beneficial than doing an endless amount of crunches or leg raises.
Generally you'll have to put in enough intensity, volume, and time-under-tension to feel sore the next day. If you're just going light on these, then that's just a lightweight workout you can do everyday.
Lots of people go out on a walk and/or a short run on a daily basis too -- it just depends on how hard your workout actually is!