Orchestral Jazz is a recognized sub-genre with a long history. Early practitioners include Paul Whiteman, a jazz musician with classical training, who combined his experience arranging symphonic music with his passion for jazz, and who commissioned composer George Gershwin to write the jazz inspired symphonic work, Rhapsody in Blue, which remains a orchestral standard. Under the influence of musical partners Fletcher Henderson and Don Redman, the sound developed more into the brass-and-piano dominated "Big Band" sound, and reached an commercial and artistic peak as part of the range of jazz subgenres practiced by jazz legend Duke Ellington, and his expansive musical empire. A more recent luminary of the subgenre is South African jazz pianist Abdullah Ibrahim, whose compositions have frequently been given full orchestral treatments.
The style in the track you referenced has a strong Latin jazz tinge to it, particularly in the rhythm section, reflecting the bossa-nova styles that originated in Brazil and gained worldwide popularity in the 1950s and 60s. Altogether, this is very much in the mode of music that would have been popular on the airwaves in the early 60s. An album that epitomizes this particular fusion is the self-titled 1967 Frank Sinatra and Antonio Jobim collaboration.
With all that said, this particular track is a relatively recent release (2014) by a production music company (Poke), featuring what seems to be a nonce supergroup of musicians best known for other genres, in a vintage style, but with modern production. Not all of the songs on the collection are Latin influenced, but they all strongly resemble Sinatra and other Rat Pack singers' work in the 1960s. If you're looking for another modern take on the Sinatra sound, you might enjoy Panic! At the Disco's Death of a Bachelor.