I think it is not mate if you play 16 Re8.
I agree -- if you play 16 ... Re8 17 Qxh+ Kf8 then you have the f7 square covered with your queen.
But to answer your question, you should evaluate your opponent's threats before making any move. If you had done that, you would've easily won this game. Good luck!
SCID doesn't do a great job of reacting either.
I was so busy on plundering offense, that I didn't notice the mate threat!