Is SOAP API becoming obsolete?

This statement is simply stating that a particular version of the API is only guaranteed to be supported for three years. In other words, salesforce guarantees version compatibility for three years. Salesforce currently supports version 20 (the Winter 11 API) through 39 (the Spring 17 API).

If you build an application today, using version 39, it is guaranteed to be supported until at least version 48 (Spring 20 API). Salesforce's current API support supports any applications written or last updated in the past six years.

This isn't exclusive to the SOAP API; the REST API, Metadata API, Streaming API, and so on all have similar notices. This means that some periodic maintenance may be required for any application that uses any API.

You can view the currently supported API versions here.

The SOAP API is not going anywhere and will almost certainly never be deprecated. You missed a key word in that documentation: version. A specific API Version of the SOAP API may eventually be deprecated, but not the API itself.