Thompson's time with the Player's League club was extremely short. He likely signed on November 19, 1889 (it was announced on November 20th), and then his return to the National League on a three-year deal was announced on December 23rd, but you can find speculation a week earlier (December 17th newspapers) that he already signed and they had to wait to announce it. There was talk in the December 10/11 newspapers that he was in Indianapolis and meeting with John Brush about returning to the National League, so he may have signed even earlier.
That doesn't mean it can't be a Player's League cabinet, but it can't be both an 1890 photo and a Player's League photo. He was basically a Player's League member for four weeks tops, and was ready to bail on the league in under three full weeks. He was already in a meeting 20 days after signing to leave. That leaves a short time to take the photo, but it doesn't mean it didn't happen.
Thompson said in an early January interview that he left the Player's League because he had no assurance that it would last, so when he received a three-year/$10,000 contract from the Philadelphia NL team, he jumped back.
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