The accepted answer is correct, but I want to add that I always heard the full rule stated as:
I before E, except after C, except words that sound like "A", as in neighbor and weigh
So the mug is just replacing the last part of the rhyme with an absurd list of other words that also break the rule, highlighting that even this rule is broken numerous times in English, beyond the additional words sounding like "A". The rule as stated above is meant as a rule of thumb, that is, not as a logically or fully complete rule, as that would be nearly impossible in the context of a simple rhyme.
The humor is directed at the English language itself and the many ways it breaks its own rules.