This was a fun question and the key to understanding what the Rokeach writes is to follow the key to his approximately 50 types of textual analysis listed in the beginning of volume one (the section on Sefer Bereshit) of his commentary.
As is indicated at the beginning of parshat Mishpatim, his analysis here is through the Sha'ar Smuchim and that is how to follow what he is saying.
His comment about not moving your lips is not central to the meaning he discusses and does not conform to the paradigm of Semicha he uses.
In that context, his comment that lips don't move when saying the twelve words of Shemot 21:24 is as @Yez suggests. It is a hint that those words are not being taken literally because it doesn't fall into the definition of true speech (that speech, which involves moving the lips is a small action מעשה קטנה) because the lips don't move.
This is also observed with the distinction between Shemot 21:23, which addresses when you cause someones death, and 21:24, which deals with injuries. 21:23 does involve moving the lips to pronounce Nefesh, which in context, would suggest financial compensation is not appropriate for killing someone. It should be taken literally.
The primary teaching by the Rokeach on this posuk is preceded by the word "וסמך" which is in two places. That the associated posukim explain what the true meaning of Shemot 21:24 is.
Verse 21:26-27 emphasizes that compensation is not literal (meaning you forfeit your actual eye for causing the loss of someone else eye). The injured party (in this case a servant) is freed.
The Rokeach's second semicha involves when someones agent, in this case a servant, kills someone. The Rokeach is saying that ones servant is equated with their ox (like Shemot 21:28). So like in the case with the ox, the owner of the ox is only responsible for financial compensation, not forfeit their own life.