This language is strange in that it has no connection to any other in its region (island of Newfoundland, Canada). Some connection to Algonquin languages has been speculated but it’s not clear and concise, I would say that if the language were a part of the Algonquin family, then it would be perhaps a very divergent member of the family. Proto-Algonquin was said to split off between 2,500-3,000 years at minimum, but Beothuk must have been a family that broke off much earlier than any of the other languages, but I don’t see the connection well at this point. The number system is completely different, there are words from contact or idea spread, but they’re not native to Beothuk. There are some suffixes and/or morphology however that could have a connection from some quick, personal observation, but it’ll never been known for sure.
This language has sounds which are not typical of most North American Indigenous languages, such as /θ/, “dr”, “tsch”, and who knows what the writers of the time meant by “dr” or “tsch” anyway? Beothuk does not have the /f/. It is remarkable that a linguist (Gatschet) was able to infer so much about the grammar in a most possible way based on the scant information available and the variances in the word-lists.
I’d be more than happy to make a video and do some research with Ojibwe, Micmak or other Eastern Algonquin languages to see if some connection between them and Beothuk could be forged but it would surely be one divergent language.