If the spur you're referring to is 93 Business—motorway spurs are perfectly fine as it's a physical construction-based classification rather than an importance-based one. There are many examples of this throughout the country, like I 8 in San Diego, Northern Parkway in Phoenix, Earhart Expressway in New Orleans, and quite a handful around Providence, RI. Regarding solely its length—considering it is a direct spur off of another motorway and isn't disconnected, it being a motorway should be fine.

As for signage, considering not all freeways have "Freeway ends" signs by their terminus it's usually standard practice to end the motorway at where there's a physical characteristic change like an at-grade intersection or when the road narrows, or at the last interchange of a bypass or where it transitions into another road.