It doesn’t matter the results of the election or the specific election, I just need to know if this means the party had no influence after the election or if they finished as a force, ie. gained power again? Is this sentence open for interpretation? Thank you so much.
The comments deserve to comprise an answer, which is that the statement means the first of your alternatives.
I suggest that the statement also implies that the Democratic Party continued to exist, even though it no longer had any national force.
Note that the construction has its ambiguous dangers, caused by the verb to finish, as exemplified by “Her education finished her as a compelling public speaker”. This statement says that after her education she became a compelling speaker, not that she ceased to be so.