I have a local interest in this. I was born in Nottingham and spent much of my life there, and, although I live in Lincolnshire, I still work in Nottingham.
Before we ask "Is this the grave of the real Robin Hood?" we need to define what we mean by "the real robin hood". I've raised this concept previously in this forum about other disputed historical figures.
One extreme: was there an actual historical person known as Robin Hood, who led a band of outlaws including Friar Tuck, Little John, Alan a Dale, Will Scarlett, and Much the Miller's Son, and who was married to Maid Marion (but produced no children?), and who was an exceptional bowman, and who stole from the rich and gave to the poor, and had a long running feud with the Sheriff of Nottingham... etc. ?
The answer to this question is a firm "No." It is possible to trace the development of the legend, and the gradual accumulation of secondary and tertiary characters from other legends. There was no "Sheriff of Nottingham" although there was a "High Sheriff of Nottinghamshire."
Other extreme: Was there an outlaw some time around the 12th or 13th centuries, with a name not unlike Robin Hood (Robert, Robyn Hood/Hode/Wood...) whose legend grew as exploits were added and exaggerated, but who in reality did virtually none of the things attributed to him? Possibly, but then...
Philosophical question: If we start at either of these two extremes, where do we define the threshold of acceptance that "our" Robin Hood existed? How many of the reputed characteristics, and which particular ones, are considered essential before we can say, "Yes, he existed" or "No, he didn't exist."
Plato proposed that if we try to define something (e.g. a table) then there is a perfect example (an ideal form) of a table that exists only in the eye of God. All of the things that we call tables are only tables to the extent that they share in the characteristics of the ideal form.
Applying this principle, the ideal form of Robin Hood is perhaps the cultural image that is shared in the minds of those of us who have read the stories.
How much did the person in that grave (or any other reputed grave of Robin Hood) share in the characteristics of that ideal form? Probably very little.