He’s not discouraged – all that running round and playing has tired him out! Your dog sounds as though he is enjoying himself. If he didn’t like being rolled over and lay on by the bigger dogs, he wouldn’t keep running over to them. He would be either clinging to you or off doing his own thing and ignoring the other dogs. Whilst he is running over and initiating the play, I wouldn’t worry. Many dogs like to play rough, especially when young.
I enjoy watching dogs interact, it teaches you so much about them and their body language. In any group of dogs (including those at the dog park) there has to be a pecking order, and at 7 months old your dog realises that he isn’t ready for a top position. Depending on how dominant he turns out to be, you may notice as he gets older that he stops being quite so ready to roll over. On the other hand, he may continue to do this for the rest of his life.
I have large and small breeds. The youngest of my small dogs always, until recently, rolled over submissively to my alpha male German Shepherd; but he has suddenly decided that he wants to challenge him! Whilst keeping an eye on them, I am letting them sort themselves out. Unnecessary human interference will only exacerbate the situation, and as long as I’m number one I don’t mind what order they sort themselves into. My other (male) small dog has never rolled over submissively, but recognises that he is number two in the dog pack so he displays different body language.
Try to learn as much as you can about canine body language, it will help you to know how your dog is feeling in any situation. The links below may help.
"Anxious" Body LanguageBasic Body languageBasic Body Language 2