It is likely there was a pool there at some point. A lower center in a round pool makes for easy swirling of debris and collection in the center to vacuum out.
It would be best to take the whole "plate" area and remove sod and dirt down to the level of the feet area under the swings. Filling in and compacting the grooves actually could be doable because you're not leveling the pool by filling them in, but I'm afraid you'll end up with some grooves in your pool floor this way.
It can take a day's work to level an area for an Intex pool, but in your case I think you may have a significant amount of it already done for you assuming the area is level to begin with.
Were it me, and this is not exactly recommended nor authorized... lol... I might try filling in the grooves depending on the soil. We have clay and have filled in a number of holes from tree removals, including an 8' deep one to the sewer. The ground sunk... about 3" total in 20 years. We've done a lot of filling and stomping to level areas of the yard and smooth out the ground under the pool. That being said, I wouldn't want grooves in the pool, floor, I prefer the dirt to collect in the center. If you're going to take it down at the end of the season though, it might not bother you so much this year and you can add more soil for next year. Your mileage may vary, always.
My blue Intex metal frame pool is on leveled dirt, then sand, with the liner on two or maybe even three tarps, the legs are on cedar fence boards, cut at about 5". We didn't have the information here when we set it up 3 years ago but we'd used the space for Intex bag pools in the past so the area had already had the weight of the water on it a few seasons. It's working well, and was not too expensive to prepare. We don't take the pool down over the winter.