First we need to figure out how much stock our competitor has got left. Go to a product page, add 9999 (or 99999) units to cart. On the cart page, it will say for example"99999 → 7891", meaning that they've got 7891 units left in stock.
Simply do this again in 24h, calculate the difference and you now know how many units they sold in 24h.
Works best with one product stores, as you only have to check with 1 product.
You can also just add 1 unit to cart, and in cart page, change the quantity to 9999+. If it doesn't update to the actual stock numbers in cart page, then it should in checkout. If it doesn't, then they simply don't count the stock.
Hope this helps.