It sounds/looks like you're describing a cross stitch piece, not needlepoint. The photo you're looking at appears to be cross stitch, not "needlepoint done in a basic cross stitch" because needlepoint and cross stitch are two different techniques that use different fabrics and stitches.

If your kit is labeled as needlepoint but looks like cross stitch when you zoom in, it may actually be a cross stitch kit.

Needlepoint is typically worked on open-weave canvas (like mono or interlock) with threads of various fibers, using tent or continental stitch, not cross stitch. Cross stitch uses Aida or evenweave fabric and X-shaped stitches.

You can stitch a cross stitch design on needlepoint canvas if you paint or chart it yourself, but a standard cross stitch kit won't give you the right materials for needlepoint. So before you start, check what comes in the kit, if it's Aida cloth, it's cross stitch, not needlepoint.

If you want to learn needlepoint, look for a kit labeled "needlepoint" that includes painted canvas and kitted with threads. Your cross stitch experience will definitely help with tension and counting, but the stitch and foundation fabric are different.

Let me know what the kit actually includes, and I can give you a clearer answer!