By means of first-principles calculations, we studied in detail the structural, elastic, and electronic properties of the tetragonal CaBe2Ge2-type 5.2 K superconductor SrPt2As2 in comparison with two hypothetical SrPt2As2 polymorphs with ThCr2Si2-type structures, which differ in the atomic configurations of the [Pt2As2] (or [As2Pt2]) blocks. We found that CaBe2Ge2-type SrPt2As2 is a unique system with near-Fermi bands of a complicated character and an "intermediate"-type Fermi surface, which consists of electronic pockets having a cylinder-like [two-dimensional (2D)] topology (typical of 122 FeAs phases) together with 3D-like electronic and hole pockets, which are characteristic of ThCr2Si2-like iron-free low-T-c superconductors. Our analysis revealed that, as distinct from ThCr2Si2-like 122 phases, other features of CaBe2Ge2-like SrPt2As2 are as follows: (1) There are essential differences in the contributions from [Pt2As2] and [As2Pt2] blocks to the near-Fermi region; conduction is anisotropic and occurs mainly in the [Pt2As2] blocks. (2) A 3D system of strong covalent Pt-As bonds is formed (inside and between [Pt2As2] and [As2Pt2] blocks), which is responsible for enhanced stability of this polymorph. (3) There is essential charge anisotropy between adjacent [Pt2As2] and [As2Pt2] blocks. We also predict that CaBe2Ge2-like SrPt2As2 is a mechanically stable and relatively soft material with high compressibility, which will behave in a ductile manner. In contrast, the ThCr2Si2-type SrPt2As2 polymorphs, which contain only [Pt2As2] or [As2Pt2] blocks, are less stable, have Fermi surfaces of a multisheet three-dimensional type like the ThCr2Si2-like iron-free 122 phases, and therefore will be ductile materials with high elastic anisotropy. Based on our data for the three simplest SrPt2As2 polymorphs we assume that there may exist a family of higher-order polytypes, which can be formed as a result of various stackings of the two main types of building blocks ([Pt2As2] and [As2Pt2]) in various combinations along the z axis. This may provide an interesting platform for further theoretical and experimental search for other superconducting materials.