From the press release on the page[0] explains they got a machine from the National Archives. Though it probably would of been more fun if they directly cooperated with citizens of the public to decode the tapes.
>While NSA did not possess the equipment required to access the footage from the media format in which it was preserved, NSA deemed the footage to be of significant public interest and requested assistance from the National Archives and Records Administration (NARA) to retrieve the footage. NARA’s Special Media Department was able to retrieve the footage contained on two 1’ APEX tapes and transferred the footage to NSA to be reviewed for public release.
>While NSA did not possess the equipment required to access the footage from the media format in which it was preserved, NSA deemed the footage to be of significant public interest and requested assistance from the National Archives and Records Administration (NARA) to retrieve the footage. NARA’s Special Media Department was able to retrieve the footage contained on two 1’ APEX tapes and transferred the footage to NSA to be reviewed for public release.
[0] https://www.nsa.gov/Press-Room/Press-Releases-Statements/Pre...