This is similar to kandyman's answer, but hopefully somewhat helpful.
First ないことはない is a double negation, so the sentence means the same if dropped:
- この店のカレーも美味しいが, 私はもっと辛いのが好きだ
So the speaker compares two curries, the shop's and the spicier, and prefers the latter. But the speaker thinks both are good, hence using も meaning also.
- This shop's curry is also good, but I like spicier ones better (or I would like it spicier).
A possible difficulty is that this also may not really be idiomatic, I guess a more proper translation would be without it: This shop's curry is ok...
To be more precise, as given in the links in the comment, this も is used to weaken the statement/express reservation on the statement, which is also the function of the double negation. As such この店のカレーも美味しくないことはない can be thought of この店のカレーはおいしい being wrapped with many maybe's.
I think in any case this weakening sense of も derives from also.
Examples for も in the 強く否定する context. They are usually translated as at all or even.
- 何もない There is nothing at all.
- 返事もしない There is not even a reply.