With angle-resolved photoemission spectroscopy, gap opening is resolved at up to room temperature in the Dirac surface states of molecular beam epitaxy grown Cr-doped Bi2Se3 topological insulator films, which, however, show no long-range ferromagnetic order down to 1.5 K. The gap size is found decreasing with increasing electron-doping level. Scanning tunneling microscopy and first-principles calculations demonstrate that substitutional Cr atoms aggregate into superparamagnetic multimers in the Bi2Se3 matrix, which contribute to the observed chemical-potential-dependent gap opening in the Dirac surface states without long-range ferromagnetic order.