This answer is about Yiddish. There have been various comments, which I build on and add to, as there are several complications:
- Does it result from a "modern migration"?
- Is Yiddish spoken in Europe?
- Is it an Indo-European language?
Let us look at each of these.
1. Does it result from a "modern migration"?
Now that the question has been clarified with a link to a definition of modern, the answer is clearly no. So it is eligible.
2. Is Yiddish spoken in Europe?
Yes, it has been for centuries, although it is rapidly dying out. So it should be counted as a European language
3. Is it an Indo-European language?
The quick answer, according to most sources on the internet, is that it a Germanic language (thus IE) with Hebrew (thus Semitic) added.
But I don't think it is fair to classify any language as IE or non-IE based solely on a simple majority. If there are significant elements from both IE and non-IE, then it is linguistically important as both an IE and a non-IE language, in my view. If we were to go with a simple majority view then perhaps the UK should be excluded from Europe based on the fact that 52% of the population does not want it included in Europe.
When we get to the question of how much Hebrew there is in Yiddish, and thus whether Yiddish makes a significant contribution to non-IE European language, I came across a problem. No easy-to-find online source in English told me. This reflects the low status of Yiddish in the English-speaking world in the 21st century.
I turned to French Wikipedia which stated that the vocabulary is 10-15% Semitic. I would say that this figure, by itself, means that Yiddish should be included, as it means there is a Semitic element in European language, even if it is not large.
But there is a much more important consideration: whereas Maltese has had no significant effect on any other European language that I can find (notwithstanding this list of words I have never heard of), Yiddish has been the conduit for a number of Semitic words to enter not only German and Polish, but also English (paying attention to those marked as Hebrew in origin) (many of which I have heard of) and French.
So, given that Yiddish is the European language which has introduced many (and possibly the most) Semitic words into English, German, Polish and French, I think it deserves a place on the list, regardless of its predominantly IE grammar and the particular percentage of words of Semitic origin.