Is 'that' required in this sentence?

The use of "Somebody" is strange: it seems like you're about to ask us to guess who it is. It's more idiomatic to say "Some people believe", or perhaps just "Some believe" (with 'people' being implied).

Once we fix this, we see that "that" is useful to clarify the meaning: consider these alternatives:

1) Some people believe that a computer able to defeat a Go grandmaster is intelligent.

2) Some people believe a computer able to defeat a Go grandmaster is intelligent.

The second runs the risk of "believe" being parsed as meaning "to believe what someone says", instead of "to hold a belief", as in the sentence "Some people believe a computer when it tells them they need to upgrade their operating system". By the time you read the whole sentence, you will have realised your mistake, and then you go back and re-read it. This type of "double-take" is a bit jarring for the reader.

Adding "that" makes sure that it is correctly interpreted as "Some people have the belief that ...", like "Some people believe that we can all live in peace".