As you may have noticed, /api/computer/{computer id} only returns core properties, and Video Controller - Windows is an analysis property in BES Inventory and License.
As your topic’s title suggests, you can use /api/query and pass it a session relevance statement to create advanced queries to return (and format, etc…) all kinds of data from the BigFix database.
There are some different query approaches, but a relatively simple one for this example is below:
(name of computer of it | “n/a”, values of it) of results from (bes property “Video Controller - Windows”) of bes computers
When passing this to API query, consider URL-encoding the session relevance. The following reference may also be helpful in case you want the output to be JSON rather than the default XML: https://developer.bigfix.com/rest-api/relevance_queries.html
https://server:52311/api/query?relevance=(names of it, ids of it,values of results from (bes property “Video Controller - Windows”) of it,values of results from (bes property “Computer Model - Windows”)of it) of bes computers
As a follow-up note, if you’re going to be performing such queries for many properties at once (I can see you already added one more in your example above ), I’d suggest having a look at @brolly33’s great post around Efficient Session Relevance Query for Computer Properties