The answer to this ruling is no. Evilswarm Excition Knight destroys Yosenju Shinchu L along with the other yosenju card(s) on the field during the same time. Yosenju Shinchu L does not start a chain because it is a continuous monster effect.
An similar example of a situation like this would be Power Tool Dragon Vs Judgement Dragon.
- (Power Tool Dragon's effect with equip cards) Once per turn: You can reveal 3 Equip Spell Cards from your Deck, then your opponent randomly adds 1 of them to your hand, and youshuffle the rest back into the Deck. If this card would be destroyedwhile equipped with an Equip Spell Card(s), you can send 1 of those cards to the Graveyard instead.
- Power Tool Dragon: If “Power Tool Dragon” and the card equipped to it would be destroyed at the same time (by “Judgment Dragon,” for example), you cannot send the Equip Spell Card to the Graveyard to save “Power Tool Dragon.”