The analysis has been taken directly from the financial statements of Southampton.
Player Trading is, as you say it, profit on player sales. Player purchases and player sales are most certainly not being grouped under operating expenses. Player purchases are amortised through the income statement based on the term of the contract for which the player was signed. And, whilst EBITDA is a nice measure to monitor cash flow, it is critical to include player trading (the profits from player sales), as well as amortisation because that reflects the cost of making transfers, which is a core component to running the business. If I run a business that is profitable, but excludes any costs from investing (of which amortisation and depreciation represent), then I will be continously required to invest more capital into that business.
Ultimately, over the 4 year period, the club has done pretty well from a profitability perspective. Nevertheless, FY2019 should make for some concern, particularly if the profit from player trading dries up, given this has historically propped up the overall profitability of the club. Club has recognised this and is now making inroads in growing its commercial revenue stream, given that matchday income and broadcasting income have plateaued.