I just don't understand why they were not included in the playable races.
I understand they don't fall into any of the groups, but there should of been a Imperial only group and they defend Cyrodil from all the people trying to take over.

Because they're the main antagonists.

Because they do not exist on this timeline. Empire is not yet found
Its not becuase they do not bleong to any groups, Its because of lore reasons

Navhkrin, you're wrong.

The Imperials are in Cyrodiil and are the enemy race. They made a deal with Mannimarco to try to keep all these alliances out of their lands but Mannimarco is kind of betraying them. So, they're an entirely NPC race.

When the lore and history evolves we might get playable "races" from the imperial faction to all 3.

perhaps in expansion.

but i doubt we will ever get imperials as an Playable Empire in TESO.

because devs wanted 3 factions, but there are 10 races in Tamriel

and since 10 ÷ 3 = 3 r 1
one race had to be excluded

and after the empire is right in the middle of Tamriel and the Emperor's Throne is some good price for the PvP winning faction they chose imperials as non-playable race

Nope .
They are not known by the name " Imperials" on this timeline.

Everywhere I look it says Imperials are what they're called. Show where it says otherwise.