Likely installing a better processor in this laptop wouldn't make much of a difference. I'm guessing you have a Pentium MMX or Pentium II/Pentium IIMMX in your Thinkpad. One that you could upgrade it to max wouldn't make too much of a difference (I don't know how fast the Pentium IIs in laptops went up to, and frankly I don't feel like bothering to look it up, but let's say you have a Pentium II 200 in your laptop and you want to upgrade it to a PII350 - this will make some difference but not really that much). I'd say grab a newer thinkpad off ebay, if you want one for retro gaming maybe find a 600E or something around those lines, or a 770-series.
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https://download.lenovo.com/pccbbs/mobiles/38xhmm.pdf