The problem with general dictionaries like the one you use is that they tend to simplify everything. To prove it lets look at difinition of "protein" in the same dictionary:
1 : any of various naturally occurring extremely complex substances that consist of amino-acid residues joined by peptide bonds, contain the elements carbon, hydrogen, nitrogen, oxygen, usually sulfur, and occasionally other elements (as phosphorus or iron), and include many essential biological compounds (as enzymes, hormones, or antibodies)
2 : the total nitrogenous material in plant or animal substances
From this difinition it is obvious that, for example, homoglobine, can't be called a peptide, since it's very important part - gem - is not connected with 4 peptide helixes with peptide bonds. Since from that definition it is clear that only peptide bonds can be seen in proteins, hemoglobine, that works thanks to other kinds of bonds, can't be called protein. Moreover, this definition is a definition of only 1st conformational form of protein, since other conformational forms have otehr types of bonds in them as well.
As you see, a definition given in that dictionary is way too simple for us to get what we are talking about. The best way to get good definition is to either look in encyclopedia, like Wiki, or in special dictionary, that is dedicated to a question you are interested in.