If not, why not?
As mentioned in this other Mi Yodeya answer here:
The Chafetz Chaim in Hilchos Lashon Hara (Klal 6, Sif 4) does give an allowance to listen to someone vent about their day, but only so that they can get it off their chest and won't go telling more people. He also says that the one listening has to be careful not to actually believe it.
From his words "in order that the speaker won't go telling more people", we see that speaking in order to vent is not an allowance in and of itself. If it were, there would be no harm in that person saying it.
Sefer Chofetz Chaim, Hilchos Lashon Hara 10:1-2, brings examples of when one is allowed to speak Lashon hara about someone for a constructive reason. One of the conditions mentioned is as follows:
His sole purpose in relating what happened must be to correct the wrong, not out of hatred or any other personal reason. (Source)
Therefore, being that speaking Lashon-harah for the sole purpose of venting would not correct the wrong of the person discussed, it is prohibited.
The Sefer Chafetz chaim Hilchos Lashon Hara, FOOTNOTE at END OF 10:14 says:
ואפשר *דהוא הדין אם כונתו בספורו להפג את דאגתו מלבו, הוי כמכוון לתועלת על להבא, ... אך שיזהר, שלא יחסרו שאר הפרטים שבסעיף זה. - It may be that if one's intention (in speaking Lashon Hara) is for the purpose of relieving the concern in his heart, it is considered for a future toeles... but he must be careful not to be missing any of the other details (conditions)...
We can compare venting, where one feels a need to relieve himself of anger and tension, to the Chafetz chaim's "relieving the concern in his heart", and consider it L'toeles.
BUT -The Masgiach Rav Yitzchak Yerucham Bordiansky quoted in the name of his father in law Rav Shlomo Zalmen Auerbach ZTL that since the Chafetz Chaim says ואפשר "maybe" it is considered a safek, and since lashon hora is a Torah prohibition the rule of safek D'oraysa Lechumrah applies here, and one must be stringent and not rely on this heter.