No. The definition of a shareholder is a partial owner of the company. Whether a dividend is paid has nothing to do with it.
Just like any company, the owners might decide they would rather re-invest the profits back into the company so it can grow instead of taking those profits as dividends. As a shareholder you have a say in whether they pay dividends, however, unless you own a ton of shares you are only one vote in thousands even hundreds of thousands of people.
A company that is trying to grow fast will often not pay dividends and use the money to make the value of the company grow. An established (some might say "boring") company that isn't expecting as much growth, but still needs to attract investors so they pay out some of the profits in dividends.