Welcome to the community. I would suggest reading through the posts on the forum to get acquainted with PicoChess. We are currently in the process of updating the code to the latest python and libraries and getting it compatible with the latest version of the Raspberry Pi OS (RPiOS), Trixie. This will be version 4 and is mainly due to the development efforts of Johan.
The previous version is v3.4 (which is the culmination of the continued development by Dirk Mollmann and others since the version that you have) and can be downloaded in this thread:
It's probably best to start there. For the DGTPi, you would want to use the Lite image. The Desktop image is mainly for standalone Pi's attached to a monitor. You'll probably need a larger SD card. Read the enclosed documentation in the archive(s) for details. If you have any questions, search through the forum and you should be able to find an answer. If not, post a message and someone should be able to assist.