Is it permitted to enter the Haneda Airport without actually flying? I know that Narita Airport has a checkpoint right after the train station, but is it same for Haneda?
To be specific, I'm interested in visiting their observation deck
Yes, the observation deck of Haneda's international terminal is the public landside area and open to all.
Incidentally, Narita stopped doing checks on entry some time ago, but even when they were doing them, they wanted only ID, not tickets. Plenty of people visit airports to meet or see off passengers.
Yes, you can enter without a ticket.
I entered that airport many times and was never asked for a ticket before heading to my flight.
I could have been lucky every single time, but then please consider that the airport's building hosts conference rooms and a wedding hall. It is obvious that at least some of the attendees will not hold a ticket.
Haneda is marketing itself as a food destination by itself. Read the reviews for this restaurant for instance, and you will find many reviews like "I decided to go to that restaurant. It is situated within Haneda Airport", mentioning they went there for the food, unrelated to any air travel.