Interesting the article mentions drinking tea while checking email - or might it say while reading TeaChat.
I think that I enjoy tea in different ways at different times. Even when doing activities on the computer, I do pause and enjoy the sip, if only for a moment. Tiny moments of tranquility. Like busy times at work, there are moments of escape as I prepare and sip my tea. Or certain cold mornings - just enjoying the warmth. Or on a hot day the gulp of cold tea.
There are other times yes, when it is more "The Way". When there is time and you can devote it solely to the appreciation of every aspect as you prepare and drink the tea. Every aspect then can be fully appreciated. Still, I do not consider this any deeper experience than in the seconds, the very moment, I stop to enjoy the tea.