No. Forced labor and genocide is not the same as a vassal state. The vassal state still has the ability to live within means, and still has the ability to separate from their masters. Concentration camps does not have the amenities that a puppet state does.
Helping = supporting.
Supporting is the aid or favor of a particular or wide array of ideas or actions. Those that support maintain a cooperative assembly, such as what Cyrodiil is doing with the Thalmor. Puppet states support their masters, otherwise they wouldn't be a puppet state.
I think you guys are confusing "support" with "agree wholesale."
You are assuming that the Empire is a puppet state of the Aldmeri Dominion. We do not know enough about the lore to confirm this yet. This thread's purpose was not only to try to find evidence of Imperial resistance, but also evidence that might prove the Empire as a puppet state and debunk the "myth" that the Empire might be resisting the Thalmor. So far, neither has been proven.
There are multiple definitions for "support". It can mean to advocate, or it can also mean to aid. This means that in a way, helping does equal supporting, but in a way it also does not.
For example, the Ottomans controlled vassal states. I am sure the vassal states did not think, "Hey, this is great! Everyone should join the Ottomans!". They might have provided tribute, resources or troops to the Ottomans when needed, supporting them in a way, but they did not support, as in advocate, the Ottoman Empire.