Yes, the Times Black credit card is a limited edition card. It is actually designed using printing plates from the Times printing machines. So, if this card is issued later to someone, it might have a different look or even be available in a plastic version.
As for why Times Network partnered with ICICI Bank instead of HDFC Bank, the reason is quite simple—business potential. Times Network would naturally prefer a partnership where its card can be sold more easily and in higher numbers.
If this card had been launched in partnership with HDFC Bank, it would have been a direct competitor to the Infinia card—no doubt about that. However, getting this card would have been much more difficult compared to ICICI Bank. Only a handful of people across India would have been able to obtain it.
So, I believe Times Network made this decision after careful consideration.