The free fix only applies to Series 2 watches in the 42mm variant and that includes all models of this watch.
The policy states that "some Apple Watch Series 2 devices may not power on or they may experience an expanded battery", and that it will service "eligible devices free of charge". The details of this fix policy can be found in document SN4534 in Apple's internal GSX portal, according to MacRumors. Operating period should not exceed three years from the date of acquisition of the Apple Watch Series 2 branded Apple store. Warranty status does not matter for this issue.
This offer applies only to the 42mm Apple Watch 2. Apple notes, however, that all models will be subject to a "visual-mechanic" inspection prior to service.
The Apple Watch Series 2 is considerably old and for some users, the wearable's battery expands. Apple has nearly always replaced or serviced such devices and generally covers expanded batteries past the 1-year warranty date, regardless of a program such as this.
In a rumoured, decidedly un-Apple move, it looks like the Big A could be about to let third-party developers design faces for the Apple Watch.
Users have experienced their Apple Watch Series 2 batteries expanding in size without any reason.