Can I use Multi-Cable Staples to run wire horizontally?
The National Electrical Code actually never mentions how to support cable. It just gives the spacing for the supports.

The supports should be identified for the use. The code section for support is below:


  334.30 Securing and Supporting. Nonmetallic-sheathed cable shall be supported and secured by staples, cable ties, straps, hangers, or similar fittings designed and installed so as not to damage the cable, at intervals not exceeding 1.4 m (41⁄2 ft) and within 300 mm (12 in.) of every outlet box, junction box, cabinet, or fitting. Flat cables shall not be stapled on edge.


As long as you follow the manufacturer's directions then there nothing in the Code prohibiting your intended use.

Good luck!