As I understand it, their photo spreads of gamers usually have the Pro Model Bat language at the top of the page. Consider:
http://https://www.psacard.com/ProBatFacts/#29hall-of-fame-players
As for the phrase "game used," it may not appear in the letter, but if the bat is graded, it gets a designation such as PSA/DNA GU 10 or PSA/DNA GU 6. The higher the number, the more confident they are that it is game used. This Jeter bat sounds like it was almost surely used by him in a game. They say that it has his characteristics and that he used it during the period when the bat was issued, but they don't use the phrase "game used bat" other than the GU 10.
http://https://www.iconicauctions.com/derek_jeter_signed___game_used_2001_03_ny_yankees_-lot81155.aspx
Lou Brock?