Are the chemical constituents of human bodily fluids similar to sea water?
Let's just consider mineral salts, since obviously sea water does not contain animal proteins or cells, and (fortunately) our bodies don't contain phages, micro-algae etc.

Sea water is very salty; on average about 0.5mol/L of NaCl (the main salt dissolved in sea water).

On the other hand, human biological fluids like plasma and the intracellular space are at least 2-3 times more dilute.

Unless some other human bodily fluids are exceptionally salty, it seems that there is a pretty big difference and it is not very accurate to say that bodily fluids and sea water have close chemical compositions. 

There are not many fluids that are very close from bodily fluids in term of composition. Popular culture tells the tale of emergency transfusions of coconut water during WWII, but that's not supported by medical literature; even though more recently, in exceptional emergency cases, it has been reported to be possible as a short term solution because of the similarity of osmolarity between plasma and coconut water.