Silly question, but exactly how do you determine that the person is beside you IF you have about a dozen "people" involved WITHOUT a grid.
To me anyway, this is no different than FLANKING in that you actually NEED to know the precise location of people involved otherwise you're just using DM FIAT to say, "ok, you two are beside each other and get a bonus".
That said...I would be surprised if the Cinematic system would be faster (an earlier concern) than either 3e or 4e since a player would be looking at 4 plus options at their turn which means they would need to actually think about what was the best option.
Okay, the Scooby Gang is walking through the Graveyard on patrol when the gang of vampires they've been hunting come out of the shadows. Two each charge in on Buffy and Angel. Two more come up from behind, one goes for Giles and Cordelia and the other tries for Xander and Willow.
The vamps attacking Angel and Buffy each get a +1 to their Combat score, while the White Hats (regular folk) of the group get a +1 to the vamps they are fighting. The GM can easily note on his scratch paper who is fighting what vampire, and for Buffy to say "Alright, I've dusted my two I'm gonna go help Xander and Willow' there's not really very much to figure out. Exactly how far away they are from each other and what angle they are at isn't important.
The game has other things to make it go quickly - the bad guys don't roll, Drama Points can help you set things up tactically rather than do them on a grid - Willow spends a Drama Point so that the vamp is standing right in front of a sharp tree branch, and Xander tackles him onto it. The moves that a character likes are pre-calculated on the character sheet, and aren't hard to do on the fly.
The fight described above would take maybe 10 minutes real time to resolve. No minis, no grid.