The number of known periodic variable stars has increased rapidly in recent years. As an all-sky transit survey, the Transiting Exoplanet Survey Satellite (TESS) plays an important role in detecting low-amplitude variable stars. Using 2 minute cadence data from the first 67 sectors of TESS, we find 72,505 periodic variable stars. We used 19 parameters including period, physical parameters, and light-curve (LC) parameters to classify periodic variable stars into 12 subtypes using the random forest method. Pulsating variable stars and eclipsing binaries are distinguished mainly by period, LC parameters, and physical parameters. Classical Cepheids, Type-II Cepheids, rotational variable stars, eruptive variable stars of the UV Ceti type, and young stellar objects are distinguished mainly by period and physical parameters. Compared to previously published catalogs, 63,106 periodic variable stars (87.0%) are newly classified, including 13 Cepheids, 27 RR Lyrae stars, ~4600 {delta} Scuti variable stars, ~1600 eclipsing binaries, ~34,000 rotational variable stars, and about 23,000 other types of variable star. The purity of eclipsing binaries and pulsation variable stars ranges from 94.2% to 99.4% when compared to the variable star catalogs of Gaia Data Release 3 and Zwicky Transient Facility Data Release 2. The purity of rotational variable stars is relatively low at 83.3%. The increasing number of variables stars is helpful to investigate the structure of the Milky Way, stellar physics, and chromospheric activity.