Stoppard is transforming Shakespeare's work to suit his contemporary audience.
The themes are the same, although stoppard has addressed them in such a way that he is able to delve into each theme further (not just surface value) but also use it as a way to show his existentialist influence.
He sure has respect for the original text, he has just taken the parts that are relevant to HIS audience and HIS purpose and elaborated on that in a way in which to reflect the feelings/attitude of the society he was in.
Keep in mind, that Shakespeare's purpose was to entertain the masses--all social classes, all levels of intellect, theatre was the only entertainment
Stoppard's audience was fairly condensed in comparison--educated people, all with a [probable] extentensive knowledge of the original text of "hamlet"
Stoppard has just chosen to shift the spot light from the nobility (higher class) to the 'everyman'. The people under control of everyone else. RAGAD also deals with how out of touch people were with God, this was post-atomic-bomb/wars and so people's faith in God was shattered. That's why, when R&G are looking for direction, this can be taken to mean that they are looking for direction from GOD. In the word game they play (the tennis one) they ask very philosophical questions, and when there IS reference to God, the other character quickly dismisses it--again a reflection of the society and it's dominant beliefs of the time.