This paper presents the SIG-Blocks system developed for automated cognitive assessment via tangible geometric games (TAG-Games). Computerized game administration and real-time cognitive and behavior assessments were realized by wireless self-synchronization in communication, decentralized hybrid-sensing, assembly and motion detection, and graphical visualization. The measurable performance data included time and accuracy at each manipulation step, overall speed of manipulative motions, and the total number of rotational motions. For preliminary evaluation, three types of TAG-Games were designed: TAG-GameA for assembly, TAG-GameS for shape matching, and TAG-GameM for memory. As a part of the game design, a computational measure of play complexity was defined for each TAG-Game based on the geometric properties and the number of blocks in the item. An evaluation with 86 participants assessed both reliability of the TAG-Game items using split-half and test-retest reliability tests and validity of the proposed complexity measures by comparing the results with three subtests of the Wechsler Adults Intelligence Scale 4th Edition (WAIS-IV), i.e. Block Design (BD), Matrix Reasoning (MR), and Digit Span (DS). The high reliability coefficients showed that TAG-Games were reliable. Regarding validity, correlations were found between TAG-GameA and BD and between TAG-GameS and MR. Behavioral analysis also showed that the TAG-Game performance was positively correlated with the manipulation speed, but not correlated with the total number of rotations applied to the blocks.