Only one small modification at line 69 ...

mDbxAcctMgr.startLink(this, REQUEST_LINK_TO_DBX); in place of this use below and it will start to work....  
mDbxAcctMgr.startLink((Activity)this, REQUEST_LINK_TO_DBX);
as mentioned here 
https://www.dropbox.com/developers/sync/start/android  

public void onClickLinkToDropbox(View view) {
    mDbxAcctMgr.startLink((Activity)this, REQUEST_LINK_TO_DBX);
}