Fact 1: Death Note exists.
Fact 2: Mikami wrote Kiyomi's name.
Fact 3: Kiyomi died.
Fact 4: There are more than 1 Kira.
Fact 5: First Kira was a student.
Fact 6: First Kira lived in Kanto area.
Fact 7: Light lived in Kanto area and was a student when Kira first surfaced.
Fact 8: The Kiras are working together.
Was Light Kira? Possibly yes considering the facts above.
Is it definite that Light was Kira? No. It could have been another student and it was Mikami who wrote the Kiyomi's name (IIRC piece of death note Light used to write Kiyomi's name was never discovered).
Fact 9: Light said, "victory is mine".
Fact 10: Light's name is the only one not written on the Death Note by Mikami Teru.
Fact 11: Mikami Teru has the Shinigami Eyes.
Fact 12: Mikami Teru called Light "God".
Is Light Kira? Yes, definitely.
So, it's not directly because Takada Kiyomi's name is in Teru's Death Note. It's because Mikami called Light "God" and Light's name being the only one not written in the Death Note.
Takada Kiyomi's wikia entry said that
Kiyomi is forced to commit suicide by fire (presumably using the fuel
in Mello's motorcycle and equipment), burning herself, Mello's body,
her belongings, and everything around her.
This is exactly like what was written by Mikami Teru in Death Note hold. This means that Mikami Teru has the same power as Kira and can be considered as one. Whether Light wrote Kiyomi's name in his own Death Note or not does not matter, because it is impossible to determine time of death down to the minutes unless you are there at the scene.
However, it is utterly impossible to fix the exact hour and minute
that life ceased unless you were there at the moment of death.
What matters is that Mikami Teru wrote Kiyomi's death and cause of death and it conforms to the her death. Mikami also write down the names of those in the warehouse, all except Light's name. Why would a Kira let one person stay alive? Because that one person is also a Kira, which is confirmed by Mikami calling Light "God"