The invitation can be construed one of two ways:
- As a gesture that signifies to China that his rhetoric on the campaign trail and over media is not fully consistent with his intentions. In this context, it's a negotiation strategy to bring China to the table and show that he is a willing partner in discussing the future.
- As a message to Xi that he must ultimately submit to America's (and Trump's) authority as the current leader on the world stage. In this context, Xi would be forced to sit through an inauguration that will be filled with "America-first" rhetoric without any ability to respond other than a smile and clapping.
Ultimately, it's highly unlikely for President Xi to attend. Despite lack of precedence, a visit from China's president would take months of coordination / planning to de-risk. Furthermore, it would pose conflicts given Hsiao Bi-Khim's attendance at President Biden's inauguration in 2021 shortly after Mike Pompeo lifted restrictions of U.S. officials' communications with their Taiwanese counterparts.