So what are the benefits of Tai Chi or Qigong during pregnancy?

Any meditative practice will have benefits for pregnancy. Here are some for Tai Chi which I, my students or friends have experienced over the years:

Relaxation
Tai Chi teaches you how to be comfortable in your body through correct alignment and posture. If the skeleton lines up correctly, the muscles are in their optimum position for relaxation. Now, as anyone who's been doing this a while knows - that's easier said than done! My body had so many bad habits when I began, that I didn't really know which one to tackle first. A good teacher will help you to work out what your next steps are for your body and its peculiar little quirks.
Pregnancy could be considered a Yin state - thoughts and awareness move inward as you focus on your body and the new life growing inside you. Whereas for many women, the normal, day-to-day attention is outside on work and obligations, suddenly there is a huge new responsibility inside. Trying to balance the internal and external worlds can feel overwhelming, stressful and not how you imagined pregnancy would be. Tai Chi, Qigong, meditation and yoga all help to balance this new duality so that you and your baby can find a harmony and flow with life together.
Tai Chi can help with sleep which becomes a little harder as your belly gets in the way. Relaxation, hormone regulation, calmer thoughts all help with aiding sleep.

Non-Impact
Tai Chi can be studied as a full fighting system of kicks punches and throws. Obviously this is not recommended during pregnancy. Just about every teacher I have met from around the world have taught beginners classes which are non-impact and train you in a relaxing medative series of movements known as 'the form'.
Carpal tunnel syndrome which can crop up in the second half of pregnancy is caused by fluid retention compressing the nerves in the wrist leading to tingling and numbness in the hands and lower arms. Yoga and Tai Chi work the wrists in a low impact way which can relieve the pressure from work related activities which can exacerbate it such as keyboarding or manual work.

Posture
Tai Chi and Qigong/Chi Gung teach you how to relieve back pain by working the spinal and abdominal muscles to hold the spine in a relaxed suspended posture. This is very beneficial for pregnancy when your growing baby is bringing more and more weight to the front of your body. Without some form of posture training (Yoga and Pilates can also help) the back can be pulled out of alignment creating problems in the sacrum, pelvis and lumbar spine. Tai Chi and Qigong movements specifically treat the waist as a joint of the body (as written about in the earliest writings on Tai Chi) which strengthens your abdominal and spinal muscles, massages your internal organs and gently rocks and soothes baby (mine seems to love it, waking up afterwards and seeming to do its own baby chi form just when I'm trying to settle down afterwards!)
The postural benefits also help with the management of ligament changes throughout pregnancy by strengthening the muscles and teaching correct alignment.

Breathing
Even as early as 15 weeks I noticed that my lungs had a little bit less room to move; walking upstairs really makes this obvious. Because Tai Chi/Qigong are about breathing into the dantien (the hara in Japanese or your core, just below the belly button) my breathing rhythms are staying deep and low. Many of my friends and students have mentioned in the past how easy it is to become breathless, breathing to the dantien helps regulate the breath, and hormones in a natural way.

Relieves Nausea
Just as acupuncture has been shown to relieve nausea in pregnancy, simple tai chi exercises can do the same. From experience this seems to be for a number of possible reasons. Morning sickenss is probably due to hormonal changes as a result of pregnancy or blood sugar changes. Tai Chi and Chi Gung have been used to regulate both these imbalances as part of Traditional Chinese Medicine for centuries.