What is a spiritual practice? This is not easy to define. The Oxford dictionary defines spiritual as 'relating to or affecting the human spirit or soul as opposed to material or physical things' which I don't think makes anything any clearer.
Is Tai Chi a spiritual practice? Who am I to answer that question? In fact....who am I? What am I? Where does this 'I' reside? Am I my body? Am I my thoughts? or something else. Meditation will, perhaps, give you a sense of otherness. In stillness you realise how busy your mind is and maybe you might percieve that you are something other than your thoughts.
Tai Chi is influenced by Taoist and probably Buddhist practices and as such has a strong meditational component. You could, in fact, say that all of it is meditation. Tai Chi is a particularly powerful form of meditation because it teaches you how to relax to a very profound degree. It is my current thinking that this is the essence of a 'spiritual practice'. Relaxing deeply means letting go of tension, letting go of fear and letting go of your 'self'.
Meditation or mindfulness in our modern capitalist world is often practiced to achieve something. It will make you happier, calmer, better, more productive etc. The original intention behind the various forms of meditation that exist is, perhaps though, not so easily quantifiable.
My Tai Chi practice makes me calmer, is that why I do it? It makes me stronger and better able to defend myself, is that the reason to continue? No it's something else. Something intangible. Something beyond words and so ,for want of a better term, something spiritual.
To me the term spiritual has nothing to do with the fluffy mumbo jumbo hypnosis of the new age. Laying on a yoga mat being told how wonderful you are is not meditation.
It's understandable that more Tai Chi teachers these days are distancing themselves from the cosmic and the mystical by emphasising body mechanics. Tai Chi is a martial art and some feel it needs it's reputation restored. I am sympathetic to this point of view. Tai Chi is best viewed as a martial art if it is to be anything else. My point is that to pacify your mind you can't have that as your goal. To attempt to reach enlightenment implies the lack there of. I'm not being deliberately obtuse when I say that Tai Chi IS a spiritual practice but is best not treated as one.
As usual, my advice would be to practice. The talking, the reading, the thinking are not the thing. When you're fully absorbed in the practice, you're in the moment, in your body....that's it!