Although some refer to this device as a "tremolo bar" or a "tremolo arm", the use of the word "tremolo" is misplaced. Tremolo refers to volume modulation. The term was originally used for instruments of the violin family. If a violinist's (or violist's or cellist's or bassist's) score is marked "tremolo", it means the player will rapidly move the bow back and forth across the string, resulting in a "trembling" sound.
"Vibrato", by contrast, is pitch modulation. Returning to the violin family: watch a violinist's left hand wiggle quickly while holding down a string. By moving her hand this way, the violinist is constantly and subtlely changing the pitch of the string. This makes the sound of the string very "wide" and "alive" -- more "vibrant."
The wham bar on the guitar changes the pitch of the gutar's strings. Therefore, it's properly referred to as a "vibrato" device, not a "tremolo" device.
Is that finger vibrato, or is he using the whammy bar?