TLDR: DAZ owns the assets but you pay for a license to use them. Always check a products license for applicable usage under "Terms of Use".
Legally speaking, buying assets like DAZ products is only buying a license to use the product which is still intellectually theirs. When purchasing you are signing an agreement called an End User License Agreement. Many of these products have a commercial license meaning you can use them to sell a product ie. your game. Usually the only stipulation is that you cannot repackage the asset and sell it directly yourself. There are many types of licenses ranging from Private, Commercial and Creative Commons (which also stipulates how it may be used). When in doubt, check the details of the particular product.
Generally stuff you buy from DAZ is safe to use to make and sell a game. This is not true of say, Skyrim + Mods which could theoretically be used to make a visual novel type game except that such licenses do not allow for that kind of use.
Read the last paragraph here for exact details.
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No you are not limited only to their assets. There are many stores which sell assets that work with Daz Studio and or Poser such as Renderosity and Renderotica. You can load up any models into Daz studio like .obj files if you have the knowhow to make it work. They also have bridge software to export their models into Blender, Maya etc which you can then use other assets within. Again, up to each individual vendor what their asset is allowed to be used for.
