It's definitely vector. It's just not transparent. The appearance is dependent on the black background that is part of the file.
Hi Danny,
to open the EPS in Adobe Illustrator is the only thing that will get the real transparent parts of the vectors in that EPS file.
Why? Because it was made in Illustrator and the original Illustrator code with real transparency is still embedded within the EPS.
You can see the creator from the header of the EPS:
%!PS-Adobe-3.1 EPSF-3.0
%ADO_DSC_Encoding: Windows Cyrillic
%%Title: b5.eps
%%Creator: Adobe Illustrator(R) 17.1
The problem is that we can only assume what RGB profile is meant for color management.
Is it sRGB ? Adobe RGB ?? Something else ???
Shutterstock should not provide EPS files like that. Just AI files with PDF enabled.
Below the EPS opened, saved as AI file, layers added and reordered with Illustrator and finally placed two times against a linear gradient fill in InDesign. Left all layers showing, right only top elements showing, background with black gradient and checkered elements not showing:

Regards,
Uwe