Yes, that is most definetly an Fm chord....however, the shape for Gm is the same only two frets higher, (begin on the third fret)
Gm
355333
Same applies with other chords, move that shape to another root (the note usually on the lowest played string) and you'll have a different chord.
Think maybe that chord site needs shooting....
Don't worry too much about me, ignore me long enough and I'll go away.