I'd say that, in a sense, any gambling tests one's mental skills. Even if it's something like slots or dice, one still needs to be patient, to keep emotions under control, to not overspend and to avoid chasing losses. All of this has an impact on how much is spent on gambling, so it's important to consider. Division into luck-based and skill-based gaming simplifies what's really going on.
If I must say, you hit it at the right spots because every single gambling games is played with a critical mindset our considering the different factors before taking a decision and it does not matter if it is a game of chance or lucks.
We may have been saying that the slot games is determined by the RTP which basically does not require skills but yet, that fact that we keep calculative focused on the game at what decision to take is some worth mental tests to be precised.
If we also talk about that of sport bet as football, it is an abundant skillful measures because doing your research and analysing the teams and key factors are all form as using your brains to do the works. So, I support your insight that every gambling games is effective to mental skills.