WoWInterface - Same mount macro

I concur. The mount information is only known by the player who called it, and you visually looking at it and finding the same one in your mount list and summoning it.

-- A NOT Possible Option
IF UNIT_SPELLCAST_SENT event fires when other players cast spells then you MIGHT have been able to use the spellID in that event in the function C_MountJournal.GetMountFromSpell. But, the event only fires for players.

-- A NOT After the fact Workable Option
Another possibility might be COMBAT_LOG_EVENT_UNFILTERED and filter out the details for the player you are looking at ( sourceGUID sourceName ) sourceGUID is actually unitid like target, mouseover etc. And then extract ( SPELL spellId ) to use with the mount spell.

Of course even that option involves you targetting them in some way BEFORE they cast the summon spell and not afterwards.

And then again, these would have to be used in a proper addon and not a macro due to the event monitoring.

-- Would ONLY work if you were both in on the trick
If your target is a friend you could both use the same addon and have that addon have a master summoner who controls which mount is used and the master person could target the receiver person and use addon messaging to let the player know which mount they have summoned the moment they summon it.
Again we use UNIT_SPELLCAST_SENT event to allow the Master Summoner to note which spell is being cast when they summon the mount.
Their part of the addon would then use C_ChatInfo.SendAddonMessage(prefix, message [, chatType, target]) to send a message to the other person with just the spellID
The Receiver of the Summon Message would then have their part of the addon use that spell ID with C_MountJournal.GetMountFromSpell(spellID) and that mountID with C_MountJournal.GetMountInfoByID(mountID) to grab the details for a spell button which they could then click to summon their one.

But then, it would be much easier to just tell each other which mount you were going to summon rofl.