Why carbon dioxide does not have the same structure as silicon dioxide?

Interestingly enough, CO2 can be made to have the same arrangement as quartz, but it requires both high temperature and high pressure. https://www.llnl.gov/str/Yoo.html and https://deepcarbon.net//content/coesite-co2-analog...

Linear SO2 molecules in the gas phase can be produced with considerable effort at very low temperatures.

The bottom line is energy. Carbon, silicon and oxygen will form the structures they do because those structures will represent the lowest energy for the combination of C and O or for Si and O.

Just an additional comment or two. While C can form a large number of organic molecules, CO2 is not an organic molecule. CO2 is a linear molecule because that is the lowest energy arrangement for carbon and oxygen. CO2 is essentially an inert gas and has little tendency to react.

Adam mentioned van der Waals forces. The term "van der Waals forces" is often (mistakenly) assumed to be the same as London dispersion forces. That is not the case. Van der Waals forces is a term that refers to all of the intermolecular forces, and includes London dispersion forces, Keesom forces (dipole-dipole attraction) and Debye forces (the attraction between polar and nonpolar molecules). CO2 exhibits only London dispersion forces, although it can be the recipient of hydrogen bonding which explains its ability to dissolve in water and to react with water to make H+ and HCO3-.

This video takes an in-depth look at the bonding and structures of two group 4 oxides: carbon dioxide and silicon dioxide (silica). The former is shown to have a simple covalent structure, where the molecules are held together by van der Waals forces. The latter is shown to have a giant covalent structure where each silicon is bonded to 4 oxygens and each oxygen to 2 silicons.

http://www.knowmia.com/watch/lesson/7239

Short answer... because Si is not C.

C is unique in a number of respects. For one thing... If you compare the total number of organic compounds and molecules we know of to the total number of ALL other compounds and molecules, there are more organic compounds and molecules.