Adding "that" before "costs" wouldn't result in a sensible sentence. Perhaps "If the matching" instead of "If matching" but there are numerous cards that look to the matching card to trigger effects, and they're all worded similarly. We'd have to alter them too for consistency, and in general, making card text longer is detrimental.
And yes, gems-only or mixed-cost including gems. Cards that reduce the player's gems as an after-effect but not as part of the cost (
Angry mob or
Mummy for example) do NOT count.