My best guess is that the curly braces are there for the parser, as some type specs can have spaces in them.
eg. An object with string keys and number values:
{Object.<string, number>}
Depending on the parser a simple type (eg string) may not need the curly braces as the parser will read the first whitespace as the end of the type declaration.
edit: Further reading suggests that the curly brackets are required, so omitting them is an error, BUT some (if not most/all) parsers will forgive sloppy type definitions if they can be handled as above.
tldr: They are important, but you can get away without using them in some cases.