I’m a little late to the party, so forgive me if some of the following has already been covered, but I don’t see how two landing parties materializing on a planet a moment apart in any way suggests that there is not more than one transporter. After all, what are the odds that two groups in two different transporter rooms are going to beam down at exactly the same time anyway?
Also, since most fans like to go with what they see and hear onscreen, then there are multiple times when we are given clues to where "the" transporter is (or is not) and they are contradictory –unless we accept that there are more than one, for example…
In “Wink Of An Eye” the transporter is implied to be above Kirk's quarters (which generally given as deck 5) because one of the characters is in the transporter talking to another character in Kirk's quarters and says “get up here”.
In another episode (I don’t recall which one at the moment) McCoy is in sickbay and via intercom to the transporter says “whats going on down there?”, since “Amok Time” implies that sickbay is on deck 5 (along with Kirk's quarters) then there must be a transporter room below.
So if we take the above two examples at face value, then there has to be at least two transporters, one above deck 5, and one below.
In “Let That Be Your Last Battlefield” it is implied that there is also a transporter on deck 5, so now we have at least three transporter rooms.
And there are other instances like the above, which are too numerous to list, but these few should suffice to make my point.
Then there is TAS , which I know for a while was not considered canon, but is once again generally accepted as such, for which the following direct quotes are specific and to the point…
The Lorelei Signal
UHURA: Lieutenant Uhura to Security Officer Davison.
DAVISON: Davison here.
UHURA: I want an all-woman security team on every transporter immediately. No one is to transport down to the planet unless it is on my order.
Mudd's Passion
SPOCK: Please, Captain.
KIRK: Check it out, Bones. Send me an immediate report.
[now in "Bridge"]
MRESS: Mudd has landed on the planet surface. Co-ordinates relayed to Transporter room four.
The Terratin Incident
KIRK: Kirk to Engineering. Scotty, can you hear me?
SCOTT: Barely, sir.
KIRK: Get a crew down to transporter room three. We have twenty minutes left while we can still operate transporter controls.
The Terratin Incident
ANNOTATION: (The crystals have retained a relative size to the crew)
UHURA: Nice to be back aboard, sir, and fitting the room again.
KIRK: All crew personnel report to Transporter rooms immediately. Prepare to beam down to planet surface.
So now we have at least four transporters mentioned.
My two quatloos worth is that “the transporter” simply refers to the main one that they use most of the time, unless otherwise specified, as in the above examples.
It’s also worth noting that D.C. Fontana was the producer and story editor for TAS, and she was also the story editor and script consultant for the second season of TOS, so it was probably she who tipped off Whitfield about the various transporters which he then mentioned in TMOST.