Everything you make up is your intellectual property, but that does not mean you could decide who gets to use it and how. Programming languages are actually quite similar in this regard. We need to distinguish several concepts about a conlang:
Inventing and naming the language, effectively means you are entitled to decide what counts as $language and what does not. You probably could even register a trademark for it in some jurisdictions. You cannot stop people from extending the dictionary or deriving a dialect, but they could probably not legally call it $language without your approval. They could still use a slightly different name even incorporating the original one, e.g. "$dialect of $language", and you could do nothing about it. (For instance, Commonmark initially was called Standard Markdown and was renamed after protests from the author of Markdown and coiner of that term, but this happened out of courtesy not out of legal obligations, and variants with names like Github Flavored Markdown or Markdown Extra remain unaffected.)
The dictionary most likely is subject to database laws which differ significantly between jurisdictions and can be rather strange. I remember a case where it was legal to read, manually type and publish a copy of a printed phone register, but the redistribution of a computer scan was prohibited. It's best to treat the word list as public domain.
The grammar is much like an algorithm in mathematics. That means it usually cannot be patented or otherwise protected.
Texts in or about the language are of course still copyrighted intellectual property of their authors. The inventor or maintainer of the language has no say in this.