You may Summon “Thunder Nyan Nyan” even if you have non-LIGHT monsters on the field, but she will be destroyed.
You can have face-down non-LIGHT monsters on your side of the field, “Thunder Nyan Nyan” will not be destroyed by her own effect, but if one of these monsters is flipped face-up, she will be destroyed.
When you take control of an opponent’s non-LIGHT monster, and you have “Thunder Nyan Nyan” on the field, she will be destroyed. If your opponent takes control of your “Thunder Nyan Nyan” and he / she controls a non-LIGHT monster, “Thunder Nyan Nyan” will be destroyed.
You can Special Summon “Thunder Nyan Nyan” with the effect of “Cyber Jar” but if you Summon another non-LIGHT monster face-up she will be destroyed.
“Thunder Nyan Nyan” can be destroyed by her own effect between steps in a chain. For example, the opponent targets your “Thunder Nyan Nyan” with “Snatch Steal”. You chain “Call of the Haunted” to Special Summon “Dark Magician” from your Graveyard, a DARK monster. The chain resolves as follows: “Call of the Haunted” resolves, “Thunder Nyan Nyan” is destroyed because there is a DARK monster on the field, “Snatch Steal”’s effect disappears because the target is no longer on the field.
If you have a face-up “Thunder Nyan Nyan” and your Set “Penguin Soldier” is attacked, when it is flipped face-up “Thunder Nyan Nyan” will be destroyed, before it can be targeted by the effect of “Penguin Soldier”.