二回 is a word and 目 is an ordinal number suffix (the part that implies the "th," or in the case of second, the "nd")
二回 has an entry
https://jisho.org/word/%E4%BA%8C%E5%9B%9E
And 目 has an entry (though you have to look at meaning #16)
https://jisho.org/word/%E7%9B%AE
Sometimes very common combinations of words and prefixes and suffixes also have their own entries, but it would be infeasible to have entries for all of them. You could make an argument for having up to the number 3 or something, but I'm sure you can imagine why we don't need 百十一目 (111th) or 一万千目 (11000th), etc.
If you ever do want to suggest a word or a change to a word, the process is mentioned in the FAQ.
https://jisho.org/faq
Ah, in my silly large number examples, I forgot the 回 between the number and the 目. Reminds me that it's worth pointing out that 二回目 is technically three parts, if you think about it.
The number 2 (二)
https://jisho.org/word/%E4%BA%8C
The counter 回
https://jisho.org/word/%E5%9B%9E
And then the ordinal number suffix mentioned above.
So 二回 is one of those common-enough combos that got included as its own entry.
二回目 isn't on jisho or it isn't a word...
So I'm learning japanese using memrise and I have stumbled across a word 二回目です (にかいめ) apparently it means "it's the second time". Now I'm questioning if memrise's official japanese lessons are legit or if this is just an error.